This seems to assume that rent controls are the only thing preventing new home construction (because of the uncertainty of being able to sell units without being hit by rent control), but supply can be restricted in many ways. The most common of which is simply running out of room thanks to natural boundaries (rivers, oceans, lakes) and local policies against building high density housing.

So rent control tends to show up in areas where rents are growing significantly faster than inflation already, meaning the rent control is at best a band-aid over the existing problem. And then the problem gets worse and economists blame rent controls.