A good Yi doesn't care about Utility.
All he cares about is the damage he does because he knows he scales better with AD than with Utility. You're getting a total of about 180-90 damage with 5 items when you can easily get that much with just two items.
You shouldn't even need MS on hit with Yi. Especially if you have BotRK.
as long as he gets resets
Key phrase. You set yourself on unstable ground and rely on getting those resets. If you don't you only get to use sheen what? 1-2 times, maybe 3 in a duel. Even then if you do get resets, it's probably still on CD.
Plus the AP lets you heal more when you meditate. Total lifesaver.
That extra 70 health (At cap heal) really is a lifesaver, isn't it?
I know it is extra healing, which is good and it can save you from that one last auto attack, but it's not giving you the impact you need.
More health never hurts. And more mana for when you start chaining tons of Alpha Strikes.
It does hurt when you can get something even better. You're right health is always a good thing but you should only build HP if you need it, and 200 HP is never really gonna be enough to make a difference. You're an ADC Assassin, you shouldn't be worrying about durability, you should be worrying about your damage so you can kill them before you even need the durability
. If you're dieing in the middle of a team fight then that means your positioning is bad. But this is all before champion roles and mechanics and all that bull♥♥♥♥.
Mana wise, you shouldn't even be using that much mana in the first place. You should use alpha strike at most 3-4 times in a full team fight. Level 18 fight, Ult, E, Q, maybe W, in total should be about 300 mana. That's 1/3rd of your total mana pool, with the remaining Qs used as gap closers or mechanically (To dodge a skill shot or damage, etc.). Sure with that build you probably will be using spells more often, but that's cause you don't have the damage to kill them fast enough in the first place. Which doesn't really set you in a good place to get those resets.
Tabi was an all right buy, Greaves or even Mobility would have been just as good.
Alacrity, Ehh okay. Homeguards would have been much more useful though if you had to defend base.
Elder lizard terrible item now blah blah blah. You shouldn't start machete on Yi in the first place though, double Dorans into Avarice blade is so much better.
BotRK pretty good item on Yi. Same with Last Whisper.
And I assume you were building IE, or atleast I hope
you were. But that should be one of your first major buys, not your last.