Hum, interesting. I think of rent control differently, but maybe the way you describe it is what is normally meant.

When I hear rent control, I hear controlled increase in rent over time for existing rental units. You make sure all rental units are profitable, but you protect existing tenants from being able to afford their rent to not being able to in a year, simply because a neighborhood has increased in desirability. So you force the market to either build new construction to profit from the boom, or to make remodeling to old buildings to justify rent increase.