I hate rent control, but I think it's a symptom of incumbents' unwillingness to allow more development, on the grounds that it would lower the value of the property they own (or more realistically, slow that value's rate of increase). A fixed-rate mortgage is basically rent control for better-off people; typically the mortgage-holder pays off a small bit of principal each month and pays rent on the outstanding amount.

So if we want to outlaw rent control, we should outlaw fixed rate mortgages too, and eliminate the artificial cap on property taxes (something that corporations exploit by using shell companies to 'own' commercial real estate, and then transferring ownership or voting control of the shell company while shielding themselves from property tax on the current value of the real estate). But we both know that that's not likely to happen.