I grew up in Tucson, a city full of garden apt complexes that in the 2000s charged $300-$600 for a one-bedroom apartment. All of them were built by private developers, owned by private mgmt companies, there were no rent control laws, and rents stayed pretty low there all the way up until the COVID demand shock.

You aren't going to ever have cheap housing in a desirable urban core, but the vast land area of inner ring suburbs can house many more people if upzoned.