The cost of building housing is generally labor + materials + land, of which the first 2 are generally don't have runaway costs as they are not an investment category.
Land is something the government can help with if they choose to do so.
The rent is tied to the price of the apt, and since housing has become and investment category, has increased exponentially.
By controlling rent, you control real estate prices as well, as investors will find it a less attractive asset.
In a free market economy, the cost of things should be controlled by a market equilibrium, so building shouldn't cost more to buy than it is profitable to build tem.
But supply is often restricted by artificial means, meaning prices go up, that's where rent control comes in.
Two wrongs don't make a right, but saying not having rent control while clamping down on construction isn't true to the spirit of the free market.
Rent control will reduce supply even more. It’s piling on another wrong.