Rank 3 upgrades are FAR too much of a power swing for how inconsistent they are distributed.

DOTA2's autochess recognized this pretty early and made it so upgrading units to tier 3 was something you could expect consistently as the game progressed. In TFT if you're against someone who got a tier 3 before you, there's a good chance you simply outright lose because of how much of an upgrade a 3 is from a 2. There's also the added problem of simply throwing your items on whoever you can expect to get to tier 3 first instead of putting them on someone you want them on. This is how a majority of my games are playing out:

Get bad/mediocre items early > lose on purpose to get a recurve bow in the item rounds > wait to use whatever items I got until i figure out who i can expect to rush to tier 3 or tier 2 in the case of epic units (usually it's nidalee, trist, vayne, draven, asol) > from here the game breaks into 2 different paths: Path 1: I got a midgame rank 3 carry or frontline unit > almost impossible to lose as long as your comp is decent Path 2: Get no tier 3s in the midgame > you don't stand a chance against the 2-3 people who do have midgame tier 3s > lose on purpose some more to get first pick in item round > hope to god you can get a rank 3 before you run out of health.

I'm not really sure how to fix this issue given how the champion numbers are fixed to their perspective pool. The only short term solution I can think of is making it less likely for people to get champions they're stacking, so that if someone else is going for the same champions, they are more likely to catch up.