ARAM Balance - Make All Champs Available

I know ARAM is supposed to be the relaxing "who cares" mode to try out champs and just have fun, but I actually find myself getting more frustrated with ARAM than with regular games just because, lets face it, there are certain champs on ARAM that are overpowered. You know there's a problem when I literally haven't met a Kennan in ARAM that doesn't completely wreck everyone on the team, just because it's so hard to get away from him and so easy for him to sweep in and take up the entire board with his ult. And he's far from the only one.

So what if, maybe, you made all champs available? This wouldn't solve the OP problem but it would make it more fair. Right now, players who play mostly mid, and therefore collect a lot of bursty champs, are going to have a leg up in ARAM, because those champs tend to do well there. And it isn't really random when you think about it - you have control over it, based on how your owned or usable champ pool looks. Since it isn't competitive, it doesn't count towards anything, and it's just supposed to be "for fun" why not let all champs be available there? It's not like you get to choose the champ you're playing as, and then it would be TRULY random.