I'm a terrible player by most measures.....

I feel like people overestimate the damage it deals. So let's say you get about 25 stacks into it, so you're sitting at 65 damage on hit. The enemy has about 50 magic resist, so it's reduced by ~35% (Very vague estimations, don't yell at me.) You're doing roughly 43 magic damage per swing as Yi. Since it doesn't benefit from crit or lifesteal it's just a little bonus damage. On a full cycle of his passive he'll deal 215 magic damage. Average ADC has ~1.8k hp at level 18, for reference. The reason flare was nerfed so hard on Yi/Xin was because the on hit health regen scaled as well, providing them even more sustain independent of their lifesteal as Xin would get lifesteal+W+Flare healing and Yi had lifesteal/flare. The attackspeed is really what he loves, and frankly one of the main reasons he's probably strong is because he is a good farmer+counterjungler with high scaling. He'll still have the traps of Yi in previous seasons which is he's a squishy melee dps that relies on picks and cleanups to get unstoppable, he's never really a straight up 5v5 fighter.

For reference, to get 25 stacks you need the item then we'll say 15 camps and 5 kills. When would you reliably get that much stacking early enough for 65 magic damage (Before resistance) to be significant? The camps are on longer respawns, so assuming you get 1 kill and a full clear every respawn you'd get that at roughly 5-6 minutes of getting every camp just as it spawns as well as a kill, this is after you get devourer, which will cost you about 2200 gold which isn't something you're going to get before 10 minutes. So at 15ish minutes you, in a perfect world, can have 65 magic damage on hit. I'd call that alright. Realistically it'd be at about 18-20 due to roaming, fruitless ganks, dragon dances, backing, not perfectly farming, etc.

Again, all extremely rough, napkin math because I don't have the patience to do serious math at the moment. I'm more scared of what a BF sword with armor pen and CDR can do than some AS and a bit of magic damage, especially on someone with good AD scaling.

It's not the late game part that bugs me. It's that its 40 damage on hit and 50% attack speed pre-10 minutes with no need to stack it up to activate like Feral Flare. It give's Yi a huge power spike to snowball faster without having to afk farm the jungle as much.