If a city in the US existed where everyone magically got their problems fixed, I imaging it would be seen as a desirable place to live, so no wonder the rents go up.

Rent is an auction, so there is a dynamic/negation about living in a place. It's not true that rents go up if "everyone is able to pay" - only if "everyone is able willing to pay"; where are competing cities with lower rents in this example?