URF champion select ideas to promote champion diversity (Discussion)

Lots of people loved URF, but didn't like the stale meta. When riot released AR URF as a solution, people complained that it was too random to the point of games being decided in champion select, or that they couldn't play (a) champion(s) they really wanted to try. So what if there was a compromise between these two extremes?

My idea: create a champion select where each player is given a randomly determined few options to choose from each match. The number of choices would be set for the game mode, probably somewhere in the 4-8 range. You can re-roll your selection, but not as often as the previous AR URF, with heavy weighting given to how many champions you own. Then everyone gets to ban one champion from the pool of champions currently available to at least one player on the opponent's team. Finally, everyone picks a champion from the ones remaining in their personal pool. Obviously queue dodge penalties are increased.

For a concrete example of how it would work, let's say you enter a champion select. Your choices are Annie, Caitlyn, Ekko, Udyr, Janna, Singed, and Yasuo. You don't want to play Annie or Janna, you're fairly certain that Ekko will get banned if he's available, and the rest don't seem very good, so you re-roll. Now you get Mordekaiser, Zed, Lux, Renekton, Nautilus, and Soraka. It goes to ban phase, and you ban Shaco, while out of your pool, Zed happens to be banned. Now you choose between Mord, Lux, Renekton, Nautilus and Soraka. Everyone locks in blind pick style and then you enter the game.

This would mean that there would only be a relatively small pool of champions available each match, the most OP being bannable, which would solve the problem of seeing the same few champions every match. However, people would still be able to pick from a decent number of choices, and after a few games you'd be more or less guaranteed to be able to pick a champion you wanted to try.

Tl;Dr: Everyone gets a random personal pool of a few champions to choose from. Bans take out the most OP champs available to at least one person, then blind pick lock-ins as usual.

Here is another idea someone had to make a better champion select for URF: Bloodmoon style URF champion select

Have any ideas yourself? Maybe a way to make my idea or the bloodmoon one better? Think classic or AR URF is better? Tired of people talking about URF at all? Discuss below!

P.S. If anyone has a good idea I will mention it up here, and provide links if appropriate.

EDIT: I was recently made aware of a slight flaw with this system, wherein a player could theoretically have all their champion's banned out. There are a couple potential solutions to this. Firstly, in case of that happening the player could simply be assigned a random champion (that they own which isn't banned). Alternatively, each player could simply have 1 additional champion added to their pool post ban phase. This would occasionally let OP picks through bans, but that also means a player wouldn't be eternally locked out of playing certain champions (such as Sona) for the entire duration of the URF weekend.