let's analyse some melee carries

GAP CLOSER:
Tryndamere: Can go through walls, not targetable
Xin Zhao: Targets enemy, gives off an AOE slow
Jax: Targets any non-building unit
Master Yi: Targets enemy

CC:
Tryndamere: Mocking shout slows those who run, makes AD champs weaker if they do turn and fight
Xin Zhao: 3 hits and you're knocked up. Also that aoe slow
Jax: Fun stun
Master Yi: N/A

if you want a backdoor champ, then TF, Xin, and Sivir would be more viable all together

Style, Wuju Style.

And this is why you build him as AP. Amazing heal, Litch-Bane procs are strong, and you still hit like a truck with auto-attacks. Not to mention highlander can reset Alpha Strike up to 4 times. Not many characters can cast 5 1:1 AP Ratio nukes that can hit up to 4 targets over a team-fight (although obviously later ones won't be hitting four).

Probably not the best mage, but great at winning his lane and works well if you have a coordinated team that doesn't mind you picking up all the kills for your highlander procs.

Bump, people just ignore Yi just like poor sivir... and karma...

lol yi is really good he's not a early game champion but late game you can destroy people yi is a auto attack champ his ult increase his atk speed to replace a slow or stun he uses speed to catch up to his enemy and kick there ass

Master Yi has no CC for a reason. He has the highest damage output in the game right now, when built right. If he maintained his damage and was also given CC he would be OP.

Why pick master yi? Because hes fast, hes that guy that makes you feel like youre standing still even though youre running, because he runs and attacks so fast, its like hes just there attacking you even though youre actually running for your live. He has a powerful steroid that resets upon killing, and makes him unslowable, he has a sort of shield that will protect him against any powerful nuke by increasing his resistances to godlike levels. Whats more, his gap closer can be used to avoid damage, and allows him to have one of the fastest jungle timers. His ganks are powerful, not many people can escape a master yi with ult and red buff, not without wasting atleast two summoner spells.

Im not saying Master Yi is better than say Nocturne or Xin Zhao, but he does have reasons to be played, I personally find Master Yi more enjoyable than those guys and would still not pick him or want him in my team for a ranked game. Hes really fun, it feels like going ALL OUT when you ult and activate ghostblade to kill someone, its really fun. Other AD junglers dont feel the same way as they dont have an ult to increase their movement speed so much.

If left unchecked he can solo towers and get away once ur opponents see you eating their buildings.

Everyone has their pros and cons:

Pros:
Fast - can't run or catch him unless you have a stun/snare
Strong jungle - with alpha strick and wuju style
Passive - Double strike makes easy FB kills (turn on wuju before using it, which can increase dmg by a huge amount)
Abilities - 2 insane dps steroids (highlander and wuju style)

Cons:
Lower health/mana compared to others
Very susceptable to CC stuns, snares, or suppressions