How I think URF can be fixed (had to remake for paragraphs)
Two sides, hardly any middle ground.
The arguments I've seen:
ARURF: Has champion variety, and is more "fair," in that the obnoxious champions aren't guaranteed.
URF: You know what you play, and games are less likely to be one sided because RNG doesn't influence the champion selection. 3 bans a team allow for some moderation.
Side Note: After looking at both of these arguments, I think the problem is that both Riot and the players tend to forget that this game mode isn't supposed to be balanced.
My answer: Obviously, blind pick leaves people unhappy (that's why ARURF exists), but trying to balance the game with ARURF just makes the game more stressful, especially when RNJesus frowns on you and/or the rest of your team.
I think the best solution is classic draft pick: three bans a team, everyone picks a champion an order, no duplicates. That way you can pick nearly anyone you want, but still have to worry about counters.