Making ARURF and ARAM more fair without removing the RNG

(tl;dr: just read the last paragraph. Do note though that I'm not going to reply to comments bringing up things covered in the skipped introduction.)

The intention behind ARURF is actually good: forcing the community to play something outside of the 10 best meta picks. The problem is the execution: between rerolls and dodges, one of the teams usually gets one or more of those picks anyway - while the other does not. This results in slightly better variation at the cost of so many games being curbstomps decided in champ select, before the game proper even actually starts.

I can understand why RIOT does not want to unlock every champion to weaken this problem - their the game, theirs the rules, after all.

But imho it could also be improved without unlocking every champion nor removing rerolls/forcing you to play the same champion even if you or someone else dodges.

How?

I believe that it could be achieved by using a system similar to the tiers' system used in the competitive scene for Pokemon games: divide the champions by their power, forming various "tiers" of similarly-broken champions, then have the RNG choose a tier and randomize picks within that tier.