I would argue that the questions asked are largely wrong. A ceiling on rents does reduce the amount and quality of housing. The question, then, is: how much does it reduce amount and quality of housing, and how much does it lower prices? If we have minimum wages, unemployment will be higher, but how much higher? On the other hand, how much higher will average wage be?

Economics is a cost/benefit trade-off. If minimum wage doesn't reduce unemployment that much (and all evidence is that it doesn't -- the US is at about a natural level of unemployment in the long term, moving up and down with business cycles), we're better off with it in place. If it kills employment, we're better off without it.