I'd be inclined to agree, but Riot has not been in favor of this option. The purported goal of itemization is, or at least was, to offer diversity of builds, and the freedom to customize the playstyle of your champion. To impose hard restrictions on what a champion can buy would therefore run directly counter to this. More to the point, though, it would be an overt admission that items as a customization system have failed, and that's not something Riot has ever truly been willing to admit.
Instead, what we've gotten over time is "stat binding", a process by which Riot aggressively tunes the stats and scalings of champions such that they can only make use of a handful of stats. Effectively, you're not forced to pick from only a narrow pool of items, but doing otherwise will simply make you lose. Riot have gone even farther by binding certain champions to certain items, e.g. by making AD assassins dependent on Duskblade. This solves many of Riot's problems, in that it lets them balance around a more controlled environment and limits the risk of abuse cases arising from players picking the "wrong" items on certain champions, all without having to impose harder restrictions, but imo is probably an even worse way of going about it: because there is nothing preventing players from picking items that are made to have very little use on their champion, the system we have is full of false choices, which are hugely misleading and new player-unfriendly, as well as a general source of frustration for people who either want to play outside the box, or just honestly do not know what to build. It's also had some pretty negative implications on balance, since the process has left many champions in a state where they are innately stilted, sometimes to the point of being almost useless without a certain item. In the case of many damage champions who were once at risk of building tanky, it's made them scale harder with damage items, thereby contributing to the hyper-snowbally environment we have today.
The larger problem at hand here is that itemization simply doesn't achieve what it had originally set out to do: it does not offer any real customization, because players mostly go for the same builds, often buying items in the same order, and rarely deviate unless in circumstances defined by pre-established rules. In the long term, fixing this may require overhauling itemization, or replacing it with some new system entirely. In the meantime, though, I agree that restricting items to specific champions may be a viable short-term solution. Paragon, a now-defunct MOBA, had this interesting system where each character had a certain set of affinities, and these affinities determined which sorts of items they could buy: effectively, you could only go for tanky items if you had a tanky affinity, or for burst items if you had a burst affinity, and so on. Implementing some sort of color-coded system in this manner could perhaps help, though League's items are also super messy in distributing stats (many AP items offer health, for example). If nothing else, going through every champion by hand, and banning certain items from purchase, could probably make for some much more efficient and direct balancing than implementing some elaborate change that subtly affects the way a champion scales with items, among other side-effects.
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