This is a really good idea, however, I think the champion pool should be somewhat larger than 30 (20 after bans). That way there's a lower chance of only being able to select from champions you don't know/don't like/are really UP on urf (like Yas). I'd say 40 would be a good number.
You only need the pool to be small enough that it's unlikely more than a couple OP picks and no super toxic ones get through.
They could maybe even add an algorithm to cause slightly better role distribution of random champ pool (between mages, marksmen, tanks, etc.). I personally enjoyed bruiser/tank/support champions the most in ARAM, while I'm sure others enjoyed adcs/mages/supports or assassins/skirmishers/bruisers, or whatever.
Also, I came up with a semi-random champ select idea for URF myself, as well as a poll for people to vote on what form they think would make URF the most fun. I want to know what you think OP if you're still paying attention to this thread after 5 months. Semi-random URF champ select