I'm wondering what exactly you are proposing, because if you are proposing locking items for classes, it would ruin a lot of what's fun about this game to people.
Jungle Karthus is fun. Taric top lane is fun. Anivia support is fun. I saw Ahri adc work on ARAM the other day.
If Riot starts locking items, I'm afraid this game would lose a lot of charm for me. There's something interesting about the theorycrafting of the game; there's something engaging about watching the patch notes and seeing what solutions they come up with for these problems.
If Riot takes that away, this game loses what makes it interesting. I know, and agree, that the balance is often frustrating, but it's also what keeps me coming back. This game is built on that idea, and I think it's working more often than not. Is it perfect? No. No it isn't.
However, that doesn't mean that we have to swing to the other extreme. Locking items into certain classes is a pretty extreme solution to what is ultimately a somewhat fun problem, imo.
They aren't really obsessed with classifications. They are trying to categorize the champions in a way that allows them to think about these problems differently, and there isn't a reason to hate on that, imo. It's a step forward; I love what they've done with mana scaling on enchanters, and I think they are starting to figure out a way to make tank supports more engaging, too. It's not an immediate process, and that's probably a good thing for the longevity of the game. The constant meta shifts keep things fresh, and I'd rather have that than a stale game with a set meta that never changed.