Yes... heavily regulated... thats why an entire generation of people live with their parents because housing costs are many orders of magnitude too expensive for them to afford. Yup. That's a clear sign that the government is putting heavy regulations on the cost and distribution of real estate.
I'm sorry, but the very premise that in our present society real estate is even lightly regulated is utterly ridiculous on its face value. As is the concept that deregulation will make housing affordable. Letting landlords and capitalists do whatever they want with all property will somehow make property cheaper? People motivated solely by profit will make everything cheaper? No, they will continue to sell property at increased costs so they can increase their profits as they always have.