The best part of Magic is that games are constantly unique. You have to adapt to different situations, and two matches between identical decks can look massively different. Every time you try to reduce the variance responsible for "non-games", you eat into the variance that makes Magic great.
The Vancouver mulligan was definitely on the right side of this balancing act despite initial concerns. It was comically obvious the first time you played with it the rule was a strict upgrade. You immediately learned mulliganing for the nuts was unreliable, and that keeping riskier six card hands was less of a crap shoot. All upside.
The London mulligan is not on the right side of this balance. My first reaction was anything but it being an obvious upgrade.
If you want the short version: the London mulligan homogenizes game play, promotes mulligans in ways that further push this, and trades "non-games" where someone doesn't take actions with "one note games" where someone takes exactly two or three actions and the other person either answers them and instantly wins or misses and instantly loses.
The Fair Side
It isn't entirely fair to the London mulligan to judge it by the broken half of things from Modern. It was largely designed to make mulligans less painful in Standard and Limited.
The problem is it doesn't.
In Limited, too much of the game is determined by raw quantity. "Every draft deck is a form of midrange" is the classic saying, and part of that is playing five and six cost cards that require you to invest five or six cards into lands. Every time you mulligan, the cardboard cost to play lands is much larger relative to your hand size. You can't hit all your lands and plays due to the lost card. Mulligans in Limited still suck with the London mulligan rule.
Same with Standard most times. Luis mulliganed two non-functional hands against Andrew at Pro Tour Guilds of Ravnica. Even if he stacked his five or four card hand he would be massively behind to a reasonable seven. I doubt any simple solution that still leaves someone down cards combats this sufficiently.
That means there are three min-max viable plans after a London mulligan. Ship your end game and hope an early curve dunks on your opponent, keep some rare that solos the game and just enough to tread water to get there, or keep no early action and hope you don't die before casting a couple heavy hitters.
This is not the most dynamic game play. I would categorize the first two categories of uninteracted aggression or rare as close to non-games, and the last option of hoping their hand is slow having a high percentage of non-games as well. The word polarized comes to mind, where old mulligan games were more mixed plans and shifting struggles against the lost resource.
So instead of non-games from turn zero, you have games where people play cards for a bit but continuing decisions don't exist or don't matter. This is just as bad, aka the Solforge problem or the Turbofog issue. It's better for people to be done with a non-game faster than to spend more time for a marginal percentage of their opponent's draw horribly failing, or to just push the variance off to later draw steps where you need to hit perfect to keep up pace. This is doubly true in online platforms where you can just queue up again if you lose fast.
Aside: this may be less true on Arena because of the ladder system emphasizing every match win. In Magic Online leagues where you just lose and instantly rebuy one bad match it is easy to write off in a session. But the Arena loss sticks to your rank. This is a whole separate discussion on why ladder systems are unhealthy, where emphasizing tilt over simple bad luck is only one piece of the puzzle.
I'm overselling this a bit. As always, the first mulligan is certainly something you can overcome in a dynamic longer game. Divination isn't three mana win the game. But five cards? I still struggle to imagine dynamic Limited games where one player started down two cards and forced themselves down a non-scrappy plan with mulligan selection.
There's also a boost to conditional cards from this mulligan rule that I really like. One of the issues of conditional cards in Draft, even pump spells, is that they are liabilities if you mulligan and struggle to find a spot to covert them to true value. Now they just go to the bottom of your library, and Limited is deeper the more reasonable but unique effects people get the choice of playing.
Aside: forcing people play a bunch of mediocre conditional cards is how you get Avacyn Restored, giving them the option is how you get all time greats like Innistrad or Iconic Masters.
In Standard it is much the same. If Mono-Red Aggro mulligans, it is looking to keep one drop, two drop, three drop, burn spell, two lands next hand. The late game is hope to draw well or hope they don't get there.
I keep using the word dynamic, and I think dynamic games are the loss here. The puzzle of how you want the game to play out is much more solved from turn zero, especially as you are incentivized to try again on hands that don't execute it well. This then echoes back to opposing hands, where they are incentivized to combat your scripted plan, and back and forth.
The London mulligan does make something like Sultai midrange mirrors way more dynamic as your sixes are more likely to recover your card with explore creatures and play up the curve, but I don't think Magic really needs to promote that specific effect more. Value bodies up the curve is already the defining strategy of Standard over the last several years.
Again, the first mulligan doesn't assure that any of this precise scripting happens, but the second one sure does reduce games to it.
I'm also thinking mostly from a player and analytics perspective. I'm sure a game where someone plays some cards, gets hard bricked, then loses broadcasts better than someone doing nothing, even if in both cases the outcome was almost certain from the start.
The Unfair Side
This is the real bad stuff.
Starting from Standard, the biggest issue is probably the high impact hate card one. The London mulligan makes it extremely probable you find a specific card. If that is a card that breaks a matchup, you can approximate sideboard games as that card showing up and both players warping everything around it.
This isn't a consistent pattern across Standard, but it exists in some spots in almost every Standard format. Cry of the Carnarium versus Azorius Aggro. Rampaging Ferocidon or some other hate against God-Pharaoh's Gift. Some swingy life gain spell against Mono-Red Aggro. Kalitas, Traitor of Ghet against Rally the Ancestors.
The reliability of these hate cards when they exist makes the idea of a secondary plan less a small shift and more of a requirement. You have to aggressively mulligan to anti-hate, or just give up on playing the basic strategy you registered two games in a match. It's one thing to have to fundamentally repurpose on your chosen strategy because they have full deck coverage, it feels shitty when it's because one card exists. And its not like you can make a format without those hate cards, because an extra consistent linear deck with no answer is bad news. Or not make a format without potential for these decks, otherwise we would have that and not Aetherworks Marvel or Nexus of Fate.
These one card wins aren't restricted to sideboard games. The extreme of this would have been Mono-Black Devotion under this rule, with Pack Rat or Underworld Connections. More recently some decks could never beat Cryptbreaker, Hazoret the Fervent, The Scarab God, Tireless Tracker. Five cards or seven, these just override any disadvantage. Again, if Magic could exist without these occurring reasonably often it would by now. Or at least the post-Mana Leak, post-Baneslayer Angel, post-Inferno Titan design era.
I think it's fairly straight forward to say more Pack Rat games is not good for the game.
After this, we leave Standard for older formats.
One thing we quickly found in testing London mulligans in Modern was decks that couldn't have a reliably good draw off five cards didn't gain a lot. It could be due to card quantity, like Amulet Titan, or a lack of redundant pieces, like Goryo's Vengeance. The first mulligan gave you one more shot, but the upgrade from the Vancouver mulligan to the London one wasn't huge. It was abusing the second or even third mulligan where stuff drastically diverged.
The decks that meshed low required card count and redundancy were the winners. Tron, Dredge, Cheerios, and Simian Spirit Guide - Chalice of the Void. None of these are really fun strategies. They also aren't unbeatable, largely because of the degenerate sideboard interplay I mentioned prior. You can sweepingly ban these decks, but are they too good on power? Can you assure that next set something else won't break this way? Are you just turning Modern into another midrange format, both with a power level chop and a push towards midrange decks finding their Fatal Push hands or Stubborn Denial hands more correctly?
The margin between linear but too consistent to be reasonable playable and linear but too inconsistent to be playable dries up real fast with the London mulligan. More unique game play is lost.
Aside: back to Standard, the decks that can win off one, two, three curves are built for this redundancy and I would expect to be able to regularly have five card hands that fire off quick beats.
Even within the context of these decks, unique game play is lost. Playing against medium Dredge and Tron hands used to be fairly interesting with the other player really judging how they can best use the extra time, and now those medium games don't exist. In testing we would mulligan every Dredge seven or six without multiple discard enablers. Few Dredge games were the slower build up games where the opponent had to figure out how quick they needed to play before things snowballed while still avoiding key points like Conflagrate. It was just a bunch of turn two eight power nut draws.
This then pushed hate cards towards the more absolute and fast, like Leyline of the Void. Sideboarded games became very scripted. Death's Shadow had two types of openers: Leyline or no. Dredge could almost always mulligan to an answer and enabler. The non-Leyline hands didn't beat Dredge sevens, but they might beat lower hand sizes. The Leyline hands won on the play via Thoughtseize on Nature's Claim, often lost on the draw to turn one Nature's Claim, or had double Leyline and it was all over. No decisions about what to Surgical Extraction, fewer about Dredge staggering damage production to minimize Death's Shadow sizing. Just binary outcomes the whole way.
Additional mulligans into functional games is also a strain on tournament logistics. Normally a mulligan to four means a quick game. If you now both mulligan more and play typical games more and (partly because of open deck lists) play into interaction more, rounds just take longer. You are losing minutes a match in shuffling overhead in Modern, and despite a much more aggressive format I would bet the average Modern match at MC London took longer than at PT Bilbao.
Now that I mentioned open decklists, that shift doubly amplifies all the issues with the London mulligan. More pre-scripted game play derived before the games start, lowered risk for aiming for the best possible hand for the situation, more mulligans and time spent shuffling even by decks that aren't linear.
The problem is the same in every case I described. Five card hands with the London mulligan play Magic, but it doesn't promote good Magic. But the London mulligan fundamentally promotes maximizing decks for mulligans to five.
How can we shift this?
My best suggestion is increase the cost of that second mulligan. The mulligan rule I would like to look at is similar to the London mulligan, but always bottoming one card and losing access to cards after the first mulligan. So start on seven, then mulligan to seven and bottom one, then six bottom one, five bottom one, and so on. This is two steps from the Vancouver mulligan, giving you both the extra card of info prior to a mulligan decision and the ability to send back any of your cards. It preserves the London mulligan in full for the first redraw, giving normal decks a better shot at keeping a closer hand, but starts to punish more aggressive mulligans. It also simplifies the selection process, similar to why Scry X Mulligan was rejected in favor of the Vancouver mulligan.
The space I haven't explore is drastic decision alternatives. Pokemon used to give the opponent an extra card (I know this is bad), there's the classic one shot cycle some cards (one shot also not great), and probably even more options along these lines. Go down a card, but then Abundance the first draw choosing land or non-land (some broken one land applications).
I get that there are a number of pressures with the changing landscape of Magic that promote a shift in how mulligans work. Arena and coverage have new demands, but from a depth of play and physical logistics perspective the London mulligan has too high a cost for too little benefit.