If Riot's going to start separating champs into classes based on arbitrary lines drawn in the sand
Then I think it's time each individual class got their own items. This isn't for our sake, it's for yours Riot, because clearly you're having a terrible time trying to balance the idea of classes in the first place (why are Diana/Nocturne not assassins? Riot: We don't know they dive? even though most assassins dive, so clearly they're divers, but LeBlanc dives when she Ws and isn't an assassin she's a kite mage according to Riot themselves so why did she get a massive boost to her damage and wave clear I mean rework during the assassin update?????????? and how isn't khazix a diver or rengar who does a literal dive and you can keep going down this rabbit hole) and the ability for every champ to build almost every item.
I personally don't think the games systems are designed to even pretend classes exist but since you're in love with idea Riot I suggest you not try to have your cake and eat it too. Let mages wield their staves, knights swing their swords and archers sling their arrows.