AR URF was created not too long ago to solve the issue of URF being unbalanced. To be honest, I think it failed miserably at that, here's why I think so.
1) Games seem to be incredibly one sided, whilst AR has clearly improved the diversity of champions you see it actually made (most) games less enjoyable. There's always one team that has the insanely broken champion who solo carries the game and the other team can often not do anything about it.
2) The "Randomness" is somewhat questionable, I've player around 30-40 URF games and there are some champions that I keep getting in champ select, for example I have had Alistar 7 times or so in champ select (not to say Alistar isn't fun). Considering I have over 50 champions to chose from that hardly seems diverse and is quite odd in terms of probability.
3) Games were more fun when you could chose your champion, when you we had a choice, at least everyone could pick a powerful champion, or at least one they enjoyed playing. Now you are often stuck in games with a boring champion who gets stomped by the enemy or just sits back and does hardly anything whilst the team mates with the strong champions carry the game.
I get that you might get bored of seeing the same champions but that's why bans were available, maybe instead of making it Random, Riot should try increasing the number of bans and letting people chose their champions. What do you think?