What evidence are you basing your analysis of the effect of price controls on housing based on?
Germany and Austria have price controls on rents, and rental housing is generally much higher quality (and, unsure if cause/effect, much more socially desirable) than say, England. In England, which has no price controls, almost a quarter of rented accommodation is “non-decent” (by the English government’s low standards) – and where 18% of members of Parliament are private landlords (not to mention those whose spouses / parents / business partners are).