While I could see why you would want this, it's not something that would take priority over balancing and patching, it would have to be more of a "side" addition, something they could work on doing while not working on patches, skins, etc. The limits for jungeling now a days are fairly small. It's honestly fairly common sense who would be a good jungler by the time you have some veteran status in the game. Experimentation is one of the best things about this game, there are many ways to play everyone, effective or ineffective, it is up to the players to find that out.
The Search bar does a fairly good job of filtering champions by letters and names. So like I said earlier, this is something that will happen over time (probably), rather than on a dime "We need this ASAP" case.
Edit: I neglected to address the other types of champions, you can see the strengths and weaknesses of these champions before matches, and see who you may or may not want to play as, I think the idea is great! Just not something that will be done, it would be such a problem if Riot made something convenient for us.