Diversity in items would probably be a major upgrade
"I need to do a lot of damage, as soon as possible. I need that damage to be AD."
If you are an AD assassin or bruiser that MUST snowball to be relevent, you build these 3 items. You also need to buy boots. That means you have 2 items left to build, and if you're smart, you're probably building a
late game. For the rest of this post, if you're an AD - you will only have 5 items slots. Because
will be taking up those item slots.
"I'm an ADC that needs to do damage over time."

"I'm an ADC that doesn't build critical strike damage to do damage over time."

"I'm a person that uses this thing called ability power, and I'm squishy."

"I'm a person that uses this thing called ability power, and I'm not squishy."

"I'm a tank, and 50% of the items you see here are only applicable at certain times."

"I'm tanky AND I do damage."

These are stereotypes that are for the most part, true. After a little under 100 you learn the basics and know what to build. But after that, purchasing anything for the class that you're playing is second nature; so familiar that you don't even need to think about it, to actually do it. Builds change hardly AT ALL depending on the match up. But what if we added more items? What if each class got the opportunity to choose between 10-20 new items? What if items from other classes, could be used for those classes? I understand the risk of not being able to balance, but what if instead, we made the game slower so that people can react? Ganks usually always lead to death now. A brawl in the lane usually means one ends up dying, rarely ever does this not happen.
Diversity is important, but how can you expect diversity when item diversity is even less popular than champion diversity? A champions popularity often times entails who is strong at the time. This means that these champions are at those peaks, superior and better than the opposing pick. This leads to a patch of them getting taken down a peg . . . and this system repeats once again.
My suggestion is slowing the game down at least 50%. This means tuning damage down severely. Then, make items stronger. And perhaps having the ability to have more item slots?