It's not so much the level of zoning, but its recent liberalization. Properties that are not living up to their zoning potential (ie you are now allowed to build something much bigger) are being pulled off the market for redevelopment. Then the new units are so geared towards ownership and investment, many being pre-sold individually, that they never return to the rental pool.

A more restrictive approach could discourage such redevelopment and sequestration, keeping rental units as rental units.