HAM is not the only reason. Canadian banks are lending insane amounts. People always say Canada's banks are "sound". Every bank is sound until land prices go into reverse.
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.
Secondly most lending decisions are made by employees. Their interests are not aligned with the long-term health of the bank. They want their bonus. Who cares if it blows up in 10 years time?
We've seen this in 2008. Banks behaved insanely.
Finally if banks were playing the long game together why pump up land prices until they are backed into a corner? Better to drip to maintain throughput.
It's not 2008 anymore. Things have changed substantially. Banks became much more risk-adverse in the wake of the burst of the housing bubble and subsequent economic crisis. The era in which loan officers are incentivized to skip risk evaluation has passed.
My point was not that there's some grand conspiracy among banks. Merely that any loan that uses real estate as collateral will be riskier if real estate prices are declining, than if real estate prices are increasing. That means that construction loans are going to be harder to get when prices are decreasing. Which suggests that the ability to use construction loans to lower the absolute price of housing is self-limiting.