Build 600K houses a year?

The fact they aren't is the supply problem.

Outside of government policies and potential to tank housing prices, is there some reason you can't build 500K+ houses a year?

Canada already seems to have an impressive rate, something like 220-250k housing starts/year. The entire US is only 1300K-1500K/year for comparison.

Is it insurmountable to just 2.5-3x that rate?

I guess the main issue is that housing lags demand. And immigration rate could also 2x on a whim by policymakers.