I fail to see how stopping the construction of housing will make housing more affordable.
Granted, I do live inside the loop in Houston and I recognize from here and my experiences in Ann Arbor concerns about only building super-fancy housing for rich people. But the solution is mandating affordable housing or thinking about clever ways to subsidize housing for working class people, or better zoning rules like cutting parking minima.
But simply stopping the construction large apartment projects in dense areas only drives up rents in the existing housing stock, which forces out working class and poor people. Or just as badly, it forces the development to the outer rim of the community -- which induces more sprawl, traffic, pollution, wasted time etc.