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Recent thought about equilibrium effects on housing:
If many people actually *prefer* denser areas, or the amenities that result from them, then shifting the supply curve right (by loosening zoning codes) leads to more housing and lower rates, but may be followed by the demand curve shifting right because the area is more desirable due to higher density, leading to more housing and higher rates. And then shifting again, until the demand curve stops shifting or you run into a steeper part of the supply curve (whether due to looser but still extant legal limits, or sheer physical capacity) so that price increases outweigh increased amenities in desirability. (Or you simply run out of ability to add people.)
So it's true that free market housing won't necessarily lower prices for good; OTOH, it does allow more people to live in a place they'd prefer, which is still good.
If many people actually *prefer* denser areas, or the amenities that result from them, then shifting the supply curve right (by loosening zoning codes) leads to more housing and lower rates, but may be followed by the demand curve shifting right because the area is more desirable due to higher density, leading to more housing and higher rates. And then shifting again, until the demand curve stops shifting or you run into a steeper part of the supply curve (whether due to looser but still extant legal limits, or sheer physical capacity) so that price increases outweigh increased amenities in desirability. (Or you simply run out of ability to add people.)
So it's true that free market housing won't necessarily lower prices for good; OTOH, it does allow more people to live in a place they'd prefer, which is still good.