Generalize that to building prices, and if true, that's going to make it very difficult to use construction to lower housing prices. Banks aren't going to lend for construction if they think making loans is going to threaten the bank's own soundness.
Or to put it another way, if falling housing prices add unacceptable risk to construction loans, then the banks efforts to mitigate that risk might include not lending if housing prices are in decline. Which means you could sweep away all zoning and NIMBY impediments, and you still wouldn't be able to use construction as a way to lower housing costs, because the banks wouldn't let that happen.