> I'm saying "increased rents + rent control not applying = more people should want to build"

This is false. People will want to build more on the margin, but that doesn't mean they want to build. If the profitability requirement (hurdle rate for getting investment from institutions) is greater than the the market rent, people will not build even if market rent is high. Indeed, that's what's happened in the last 5 years as costs have increased much faster than rents.