>The second would be if the sale price dropped below the nominal price of construction new units, with some wiggle room in there for opportunity cost to builders who might make more money by choosing to build elsewhere.

You also have to factor in the opportunity cost of the land/unit too which is where the argument starts to fall apart. Why build a unit that rents for $X when you can increase your build costs by Y% and charge a rent higher than $X + Y%. That is why new construction generally comes in at or near the top of the market. Construction costs generally don't make up most of the costs of new homes in places like San Francisco, Chicago, or Los Angeles.

But sure, if you want to create a world with no zoning laws and with 10000% increase in housing supply, I am sure it will solve all the problems with pure brute force.