That's definitely not how it works. You can't just choose which miner will process your transaction.
Yeah, if I want my transaction to be picked up by a miner who doesn't require fees, I can just sit patiently.
What? A miner that accepts transactions with no fees is not actively blocking transactions with fees. This point makes no sense.
This is all based on your assumption that miners will start leaving, which simply isn't true. There's no motivation for them to leave.
Miners leave all the time when they're no longer profitable...
Why are they no longer profitable? Your hypothesis about people not wanting to be with them (which, how will they choose? You CAN'T CHOOSE a miner) is incorrect.