Master Yi is a terribly designed champion
...But not for the reasons you might be thinking of.
Part 1: Alpha Strike is broken
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In principle, you're supposed to see spells about to hit you and press Q to dodge them. This does not work correctly because there's a cast animation before you disappear and become untargetable. It's short, only about a quarter of a second, but it's enough to make "reactionary" Alpha Strikes very unreliable. It also causes weird interactions, like when stuns hit you mid-animation, you disappear anyway, and you're stunned when you reappear.
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The untargetability duration varies wildly depending on how many targets you have. If you're in the middle of a minion wave or teamfight, it takes about a second to reappear after casting Q. If your target is isolated, you're untargetable for barely any time at all. This can be helpful depending on the context - for example, you kind of want to be untargetable for a long time in teamfights so that you take less damage. But in many contexts, this is very bad. You have very little control over the spell. Suppose you're ganking an enemy champion, and they're sort of near their turret and minions. You can't use Alpha Strike in this situation because the targeted champion will walk to their turret during the long animation and you'll take turret fire. Or worse, they'll Flash and you'll be forced into a turret dive. This is also a problem in opposite situations, where you're dueling a completely isolated enemy. You're trying to dodge one important spell with Alpha Strike, but it's tricky because your Alpha Strike will only make you untargetable for a small fraction of a second, leaving you with a very small margin for error. This is where the aforementioned cast animation is really frustrating, you can time your Alpha Strike "correctly" but still get hit by the spell you were dodging.
Part 2: Meditating is useless
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Suppose you're low on health, or otherwise in danger, and you're trying to heal with Meditate. There are so many things enemy champions can do to counter you. They can interrupt you with almost any kind of CC, and they can apply grievous wounds.
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The healing from Meditate is so bad during midgame. It's the spell you max last, so from levels 3 to 13, you're relying on rank 1 (sometimes 2) Meditate. The damage reduction scales naturally with your health and resistances, but the healing does not scale (except with AP). So around level 10, most enemies don't have to do anything special to kill you through Meditate - they can just outdamage your healing with brute force, without CC or grievous wounds.
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To add to that, Master Yi is a melee fighter. He can be kited, and always needs to be moving. During the time you channel Meditate, you're standing still and ranged enemies walk away from you. Master Yi is not lightning fast; it takes time for him to gapclose again, and during that time, you're usually taking damage from enemies and rapidly losing health. Which brings me to part 3:
Part 3: Highlander is worse today thanks to nerfs and mobility creep
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During the Sated Devourer meta, Highlander was nerfed - the base duration went down from 10 seconds to 7. This was a surprisingly painful nerf, even though it was compensated so you get 7 more seconds (up from 4) now with every kill/assist. This hurt because now, more often than ever, Highlander can just end in the middle of a fight. Similar "super mode" ultimates last much more than 7 seconds. Aatrox - 10 seconds, Dr Mundo - 12 seconds, Nasus and Renekton - 15 seconds, Shyvana - 20+ seconds, Singed - 25 seconds. I know what you're thinking: Master Yi can get resets to make his ultimate much longer than 7 seconds long. And you're right! But that first kill is always the hardest one to get, because so many things can delay you during those 7 seconds. Enemies run/dash/Flash away from you, CC you, protect themselves with Zhonya/Stopwatch, disappear with stealth - and on top of all that, it can take several seconds just to deal enough damage to kill an enemy once you've got them. Master Yi doesn't kill enemies instantly, at least not usually. It depends on a lot of things like what build he's using, stacking requirements of his runes/items, how fed he is, how squishy the target is, etc.
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Highlander is not fast enough to keep up with the action anymore. Highlander has to be fast (relative to the champions he's facing) for two main reasons: he needs to be able to stick to enemies even while stopping to autoattack over and over, and he needs to be able to gapclose with Highlander. Alpha Strike is Master Yi's main defensive spell (because Meditate can't protect Master Yi from most damage and CC), which means that he can't use Alpha Strike until enemies have used their important cooldowns. Things like Lux Q, Neeko E, Pyke E - you can't use Alpha Strike until after those spells are cast, you have to use it reactively. You're also using Alpha Strike to react to enemies using Flash or other mobility spells to get away from you. Which means that more often than not, you're relying on Flash and raw movement speed to gapclose on enemies while you wait for the moment that Alpha Strike is needed. Now, if you play champions like Udyr or Volibear, you know that having high movement speed is important in teamfights. Being faster means you get into the fight quicker, and you spend less time in the 150-800 range space from enemies, where they deal damage to you and you don't deal damage to them. For a champion like Master Yi, who's typically almost as squishy as an ADC, spending just a few seconds in the 150-800 range space is DEATH. Getting back to the mobility creep issue, more champions than ever can move juuust fast enough to match the speed of Highlander. Remember, Highlander only gives 25/35/45% movement speed - that's a lot lategame, but consider how many champions now like Ekko, Katarina, Lucian, Rakan, and Lulu can match that, if only for a couple of seconds. Not to mention items like Deadman' Plate, Ghostblade, and Phantom Dancer, spells like Heal, runes like Phase Rush and Celerity, and mechanics like Cloud Dragon that have affected the pervasiveness of mobility over the years. Remember, you enemies have to run faster than Master Yi. Just fast enough that he can't chase and attack them at the same time.
Part 4: Wuju Style doesn't do anything
- This is a pretty minor thing compared to the points above, but this points to a larger problem with Master Yi as a whole. Everything he does is just damage with basic attacks. No utility, no range, nothing but damage. This is frustrating for all players involved. Master Yi's opponents don't like fighting against a champion that can potentially melt their entire team in a few seconds, but when Master Yi is just a little bit behind, it sucks to be so useless. Whether Master Yi wins or loses, somebody is having a miserable time. This makes him a pain to balance, and it's a large part of why he's great in low elo and almost always bad in high elo. Damage is king in messy, unorganized games, but good players can see that Master Yi has very little to offer to a team. He's basically the opposite extreme of Azir, Lee Sin, or Irelia, champions that dominated high elo because they could do everything.