random ascpet of snowdown urf

I was excited that urf came back to say hi as i never was around for normal urf and ar is just enough to get me by. I was curious though one day after playing a lot of urf as to what champions were active in this mode and went onto the wiki. I saw roughly 60 champs but ive only seen the same 20 like fizz or nidalee, syndra, or dravyn for example. then about another 10 i see rarely like singed ive only seen 2 times in all of my snowdown games. I like the ar aspect of things to this mode riot but not the chances of playing the champs. If every champs had the same percentage of being randomly picked, would it not be good? was this tested before or has it not been tried? cause i always view urf as the chance to do whatever build especially with the new runes system in place that becomes much easier, but i was just wondering about this was all because i think i would enjoy a bigger variety of champions each game, not a bigger number with some having smaller percentages of being picked compared to others. lemme know or maybe the community will let me know if this has been done before or talked about before.