ARAM Ranked but you choose your champion
It would be very interesting to at least try in PBE. The meta would be completely different, "objective control" would be obselete, and overall would be kind of cool to see which pro players do and don't make it to the top of the ladder. Just make a ranked ARAM where you ban champions and then choose champions the same as in ranked normally. Queue times would be nonexistant as roles wouldn't be picked. There's ranked solo/duo, there's ranked twisted treeline, why not in ARAM too if done correctly?
Meta would definitely be focused around poke mages and ADC's with the occasional tank or utility support. Tell me this wouldn't be fun as hell.

