The trick is to combine it with the state creating housing supply.

That's what Vienna does and it's famous for its low-cost, high quality housing.

The city of Vienna is Europe's biggest landlord. It's also the most livable city in the world for something like a decade in a row now.

The moral problem with rent control is that it prevents people discriminating on price, so they discriminate on other factors (colour? sexuality? Age!) instead.

There are others too, but that'd the most glaring...

That's my biggest problem with socialism in general, it replaces "This person is willing to pay me more" with "I just like this person better" or "This person has the right connections." Of course there are situations when "This person is willing to pay me more" isn't fair, but those other things are even more unfair.

The nice thing about the highest bidder gets it is that is creates an incentive and resources to make more of whatever "it" is. Capitalism isn't meant to be fair, it's meant to make more. That doesn't always work, housing is a good example of it struggling, but it at least tacitly tries to solve the core problem (shortage).

How does rent control limit supply?

The owning class (Both single home owners that live in the house they own AND people who rent out units) already fight against the building of additional supply.

> The owning class, already fight against the building of additional supply.

I mean of course, but both are true, it limits supply in just the straightforward way that it means more people can compete in high desirability areas. (maybe it increases demand, not limits supply?) either way it drives prices up.