How about PvE URF?
Where it's actually designed to be interesting. We'd get to pick our champs this way.
I like the wacky cheese and mowing people down in URF, but that comes at the expense of whoever you're melting, and if they're doing it to you it's kinda dull. Not a lot of great duels in URF, just people getting bursted. I propose PvE Urf as a way to have your cake and eat it too.
Urf players vs a swarm of bots with some buffs that make them a threat in large numbers, and the revive/tp advantage that doombots get. Maybe two dozen bots, so there's 8 in each lane. Point being that fighting them isn't totally brainless, but you should have a fair shot at mowing them down. It'd basically be the 100-man melee from smash bros.
This way we can try random URF crap and 1v15 gloriously, without having to sit around bored because the enemy eve/shaco decided you dont get to play video games.
Edit: I don't propose any particular way to implement the bots (giving the bots the Urf buff would be unwise, for example). 5v24, or give them some improved version of the Doombot buff, the important thing is to create an engaging PvE experience to use the Urf buff in. My current thought is to bring over the bullet-hell aspects of Doombots with increased range but reasonable cooldowns, and have them instantly respawn and tp when killed to keep the action going. Basically just give them anything that would be fun to play against as while using the Urf buff.