In your hyperbolic, unrealistic scenario, are the ultra-wealthy going to be permanently renting?
They're doing it for the short amount of time it's going to take for them to buy another mansion - they're in the rental market because of a disaster. Once they've recuperated, they're gone.
But let's say your exaggeration comes true. Do you think landlords would be able to continue renting for 5x the amount once their ultra-wealthy market dries up?
You seem to think I'm a proponent for the price gouging practice, so I'll reiterate: I'm not arguing that the problem should be ignored, and something needs to be done about it.
I simply have no sympathy for those looking to rent where a 20% increase equates to $3000 a month.