As a Yasuo main that also plays Yi, I really agree with you.
Master Yi is not a very snowbally jungler. He's actually a mix of all the 3 kinds of junglers: he can gank, he can counter jungler and he farms pretty fast. But in all of those, he's a very situational pick on what kind of jungler he is. For the most part, he's a farm reliant jungler and since he has no CC, he has to either provide pressure by continually gank post-6 but by that, he can get very behind if he doesn't get something done in his ganks. If he farms too much, he'll have the possibility of neglecting other lanes. He can counter jungle yes, but in very specific situations and against the right jungler.
Because his kit has no CC and no reliable gapcloser (other than his R and Q but Q is mostly used as a finishing tool or for untargetability and not an engage), he has to play smart on how he approaches his target. He plays like Yasuo in the sense like what OP said: Risk Assessment. He first points out the CC the enemy has that can shut him down or the number of enemies that has a dash or blink that can deny him his resets. However, Yi has all the options needed to abuse those windows of downtime in the enemy's CC or mobility for him to get good picks.
Unlike most other melee carries like Yasuo and Fiora, Master Yi is much more feast-or-famine than the other 2 because no. 1: he has a weak early game and no.2: he is reliant on the fact that the enemy jg will not counter jungle him nor will he pressure out multiple lanes or even objectives. In low elo, this weakness is partially removed since junglers around low elo don't play as smart as most other players but in high elo, people will take any opportunity to deny Yi's chances of making picks nor allow him to get his items. I think this is the reason why Yi, ranked-wise, is unhealthy because in low elo, he's freelo but in high elo, he's very easy to stop. I could be wrong here since I've seen players like Cowsep who can play Yi really well in high elo.
But overall and mechanics-wise, I think Master Yi is healthy, but requires a little more tuning or probably a rework. He's becomes too much of a monster when fed or complete garbage when denied him his opportunities of getting gold or picks. The fact that he sacrifices CC for a carrying-style kit is also something to note about him. Not having CC means you have to be completely devoted to deal damage for your team or else you're going to lose a lot. But I don't think that's a bad thing. CC is important yes, but what is CC w/o the damage needed to follow up with? (lol this is why team comps exist) I think it's fine for Yi to have zero innate CC in his kit but has a much higher amount of raw DPS than most duelists or other melee carries.
prick does everything better while also having more burst hell an eggplant with a stick(
) is better in every way to yi
, usually selling boots for 
or 
late game.
