Personally I prefer to play Yi over Noc, Xin or Tryn Since (1) Noc might deal a good amount of damage end game and is fun to play but his DPS isn't too phenomenal, also I find your mainly cleaning up after other's not really solo'ing. (2) Xin is awesome, having a bit more armor imo than Noc or Yi but at the same point in time most gear that your purchasing for him is expensive causing you to farm minions/monsters more opening you up to full on ganking from the other team since they are more threatened by you. (3) I know that Tryn is awesome but personally I suck at him...

Yi is an all around fun Champion to play as, And anyone who plays multiple Champ's knows he has a higher Crit early game and is almost unstoppable end game... Those who feel he sucks or doesn't like him obviously doesn't look at the Yi Build's, You want to look at those and then create your build off of the proven ones that works for you... Yi is NOT a tank, and can easily be killed if not kept up level wise but as everyone knows the resolution to that is Minions/Monsters. Just my two cent's which doesn't mean much considering I'm relatively new to the game vs. most of you legends.

Oh that's easy because Yi typically backdoors really well =p

Jax harder to play, need dodges
Xin doesn't do as much damage as fast
Trynd, does more damage but dies fast

Yi has the highest DPS in the game, thanks to a lot of free stats he gets. He's a capable melee champion from early to mid, and then he's a very successful backdoor champion.

Why not? Some people like the champion and doesn't care if it's "viable" or not. It's not like they'll have a 100% lose rate with Master Yi.