How i would balance URF (WARNING: this is my opinion, dont get your knickers in a twist.)
If i could balance URF for the next time it comes around i would do it this way:
1# If its going to be ARURF: A ban phase where each player gets 1 ban, the game then chooses a champion for you from the ENTIRE champ roster that isnt banned. If someone dodges because he got a champ he didnt like, the game gives him the same champ again the next time he plays. If you used your reroll and someone dodged, you will be given your reroll back.
2# If its going to be regular URF: A ban phase where each player gets 1 ban.
3# If possible, make both types of URF available in both normals and custom. This way everyone gets to pick theyr poison, do you want to play a relatively random mess where you dont get to pick your champ or a tryhard filled mess with people that will gravitate to the next best thing after the top 10 broken champs get permabanned.