I read your entire comment and despite being three paragraphs long I can't see how it addresses gp's point, which is that the scarcity is still there whether you institute price controls, and instituting price controls only changes the symptoms.
Housing is not scarce though, some people (companies) own 14 houses whilst others have non. It's not a problem rent control can solve, but it's also not a scarcity problem.
Some companies owning 14 houses is not evidence of abundance.