Rent control or not, the law of supply and demand still applies; it just expresses itself in more dysfunctional and unproductive ways.
That's the problem with rent control. Reasonable people can disagree about whether the public policy goal of getting people affordable housing trumps the rights of property owners. But they can't disagree about how many digits are in pi, or about whether rent control works. It doesn't work. It harms everyone in the market except for a lucky subset of tenants.