ARAM and ARAM accounts

I'm sure this has been suggested before but I'm curious what the reason is for not doing it. Why not factor total champions owned into ARAM matchmaking? I may just be overreacting but seeing 5-6 champions show up game after game (while not on free rotation) makes me suspect players are manipulating the champion pool to make it a little less random. I know Riot said they were wary of unlocking all champs for the mode, but by accounting for # of champions owned it would level the playing field on how random your champion actually is. To be clear just using fairly large ranges would probably be good enough to distinguish players trying to game the system from players taking a break from summoners rift. I assume that new players would get separated out by the same method they currently are.

Edit 1: Yes I realize lower ip champions appear more often.