There is one reason and one reason only why this will more than likely NOT happen, and it is two words: Vote Manipulation, if a contest like this was to be held dollars to donuts says the winner will be the one that is most liked by the players. And that is tricky to pull off because we are using a reddit upvote/downvote system, so as such people who entered will just end downvoting the others so their get more view traffic/get multiple accounts (either ones they've made or from friends that aren't gonna bother to enter) upvote their idea/downvote others so they get more attention. And if it's like an actual vote based on something like a poll and not by Reddit system then the manipulation can still occur using the latter option in how to manipulate the Reddit System by having friends upvote their idea.
And before you ask "then why won't Riot do the judge system then?", it very simple, because it matters if riot were to do it. With the CCOS there is no reward large enough that everyone wants to win it, and everyone who does enter already wins attention on their concepts, which leaves everyone satisfied. But imagine how much anger, how much hatred, how much whining will occur if a concept that they wanted didn't make it/a concept they despised won, and now they will have to wait a whole year or some extended length of time to try again? It just too much salt for a community that has their fair share of toxic people in it.