The interesting thing is, they have done a few things to "balance" some champions in URF.. or rather, ARURF, .. but they only seem to be buffs.
For example, Aurelion Sol gains stars by level, reaching 5 instead of only 3.
Evelynn can spam the spike portion of her Q until it comes off of cooldown. I think I could usually get around 12 off before I had to use the skill shot portion of it.
... I'm sure there are others, .. but I can't think of them, .. or I simply haven't experienced them myself.
I do agree though, there are some champions who could probably stand to be subtly nerfed in URF (hehe that rhymes).
The one that comes to mind for me is actually Tryndamere. LITERALLY EVERY FIGHT he can become unkillable. ... That is not really fair.