Suggestion for how champions are chosen in ARAM and/or ARURF

Random idea for ARAM. I think the current way it works is just bad (not fun). You get 1 champion chosen out of the current champions you own + daily rotation, I think this could be changed to where you get 5 champions, or X amount, to choose from rather than being given 1, and it's not limited to your owned champions.

I know there are obviously people who want to stick with their pool of champions etc, so it would be cool to see other peoples suggestions. Maybe this could be put into ARURF instead, since getting a champion you don't like or just isn't good in this mode can really make it horrible.

Thanks.