[thinkharderdev]

The supply of land is (mostly) fixed but the relationship between land and housing units is not. You can build row houses or multi-story apartment buildings instead of single-family homes, so the supply of land is almost never the binding constraint. What is a major constraint is various restrictions on building additional housing stock (and particularly building higher density housing stock) but that is a malleable constraint. Given that constraint maybe price controls on housing aren't so bad but still having an equilibrium where there is dramatically more demand for housing than supply is bad. Either you get sky-high prices or you get rationing through other means (you can only get a rent controlled apartment if you have connections or just get lucky).

[imtringued]

That's an argument for (land) taxation, not direct control of prices.

Here is an idea: Measure average rent per sqft. Put a 20% tax on rent above the average and use it to subsidize low income households. That way you tax wealthy tenants and subsidize poor tenants.

[epistasis]

Yes, I agree on all this. But rent control is about price changes on existing houses, not on new construction, at least in the US.

So it's not a "price control" as much as it is a control on rentierism, on existing rentiers taking unearned profits without working.