Rent control is the quickest way to destroy the city’s housing stock. It is a misguided effort to provide relief from the cost of housing. But as you correctly intuit, why would a landlord every buy a property if he could not raise rents to keep up with rising property costs — especially property taxes! And what landlord would make improvements for tenants — from a new refrigerator to painting the hallways — if he/she could not get the cost of the improvements back through raising the rents? You’d have a city of increasingly dilapidated housing and no incentive to fix it!
But the real and very immediate issue with buying property in Chicago is the fact that real estate taxes MUST rise to deal with the city’s oncoming pension crisis. Or there will be some other kind of tax. And the situation with Illinois is even worse — so you would see higher income taxes if you lived here. I love Chicago — but I can think of a dozen other states where it makes more sense to invest in housing.