Sure, but they'll all be on an even playing field. If Alice rolls a champ she's never played before, there's a decent chance Bob on the enemy team is in the same situation. It's also pre-30 games, when people are expected to still be learning about League.
Personally, rather than simply unlocking all champs, combining individual champ pools for all players in a given match seems better. Pre-30 players would only have to deal with a (presumably small) subset of champs, and ARAM players would still have a reason to buy champs. Not sure if it'd work for technical reasons, but it's an appealing solution to me.