Random *can* be balanced
Just because each person gets a random champion from the ones that are available, doesn't mean it can't be balanced for the team. It would mean that riot would have to remove re-roll, and base the random on roles. There is no reason that one team should have no ranged champions. Or no AD. If you think it can't be done, then you just haven't thought enough about it. Of course it could be you can't think at that level ... that is always possible as well