>And do you think prices have to increase so that you can have an "artifical oversupply" of housing?
No, prices and rents in the most desirable areas should creep down toward "the marginal cost to create housing" as we create an oversupply. It will never actually get there, because people will need/want to create a profit, but it should find its way toward an equilibrium near there.
The only reason why they might bump up temporarily is only that new housing is more expensive than "used" (existing) housing, so when new housing comes on the market it, it becomes the most desirable, and is priced the highest, but that should reduce the price of existing housing.
This is your basic supply curve, though many people will argue (without much sense), that supply curves somehow don't apply to housing.
>And I thought you were advocating for free markets, yes, since you talked about "market rate". Sorry for the wrong inference.
I'm a strong believer in markets generally, though not necessarily "free" markets, because I think incentivizing and disincentivizing things we collectively want/don't want is one of the best ways to create general welfare for most people.
The reason I advocate for markets in housing is two-fold.
Firstly, housing is notoriously easy to hoard and sublet, which makes it ripe for abuse in a subsidized system. If we give people housing at significantly below market prices (that is prices below what they could get an equivalent unit for today), we should expect "dishonest" people to sublease that housing to capture that value. This is commonplace in San Francisco, where I live, that folks with rent-controlled units regularly bring in roommates or subtenants and charge them market rates, and just pocket the difference. Yes it's illegal, but it's a civil matter, and would require an expensive lawsuit against your roommate to solve, which would then likely end up with you looking for another unit at market rate anyway, so it's impractical to enforce.
The other reason is land-hoarding. As we see in Stockholm, and in long-term rent controlled tenants in San Francisco, we see people paying below market rates, and then they tend to have more space than average. This is simply cause by the fact that, all things being equal (in price), more space is desirable to less. So this is a major inefficiency for everyone else who needs housing and would be willing to settle for less space. My utilizing markets, we will see people more willing to use space efficiently being allocated more units.
This is why I want to see markets (or at least lotteries), with at least semi-regular lease renewals, even in socialist systems. When housing isn't perpetual, people will vote to provide that good to everyone, and not just themselves (especially when difficult trade-offs must be made to do this). I want people to have skin in the game, where they know that if we aren't taking care of everyone, they themselves are at risk of being left behind.