Most people just want a balanced playing field. Like it or not, being under level 30 means you will be missing a lot of runes, masteries and champions. I do not want one team to steamroll the other due to artificial disadvantages like these.
I do not know about anyone else, but I'm always suspicious of low levels. To me, it means they are new and probably not very good, are low level because they remade a banned account, or are a smurf account just for ARAM games.
Any one of these can ruin a match for one team or the other. Now, I know ARAM is rarely balanced and is "just for fun" (fun is subjective, by the way), but sue me if I want a half decent game that is not a complete stomp either way.