How about making the items themselves random, but the amount constant

For example, I think it would be beneficial that after each stage with either minions or monsters where currently you only have a chance of getting an item, you are guaranteed to get a popup that let's you choose between 2 random items or some bonus gold.

In this situation, the items you get are still somewhat random, which will maintain item diversity across players, but it gives everyone the opportunity to build items, not just those who got lucky and received 3 at the start. But let's say that one person's pop-up keeps on giving them the same item that they don't need because the system is still random. Then they have the option to choose the bonus gold choice, so it is up to them whether or not they want an advantage in champion tiers, or in item completion.

I feel like this alone, and maybe some changes to how the champion pool works and matchmaking is what TFT really needs to be more enjoyable.