This argument presupposes multiple levels of assumption. By the point where the assertion is made that construction costs would drop, the prediction's error bars equal the entire range.
There's no reason to believe that construction companies would accept jobs at prices below the cost of materials and labor. Construction companies frequently let workers go rather than accept large negative cash flows.
There is no assumption that construction costs would drop. The premise is that construction activity would decline until the lack of construction induces enough scarcity for even rent-controlled properties to cost enough to justify construction costs.