But RealPage isn't a supply issue? It's easy to price gouge consumers because housing is inelastic. And the fine they got is a slap on the wrist!
Price gouging is more widespread than one isolated price fixing case. It's easy to achieve in an inelastic market. As one example, moving costs money so rentiers can raise rents as long as there is a switching cost to moving. Deregulation doesn't address the fundamental inelasticity of the housing market.
Your comment also seems to be oblivious to the role that interest rates play. Mortgages are not corporate-owned in the sense of the parent comment, but mortgages are a cash flow from home owners to corporate financiers - a cash flow from the working class to the wealthy. ZIRP led to high prices; with rising rates, homeowners are incentivized to hold on to their properties rather than move. These are issues of macroeconomic finance and wealth disparity, not "building codes and zoning".
While you're right that the parent's comment of corporate ownership of houses is off base, multi-family housing is majority corporate owned. Multi-family housing is a huge portion of the housing market, particularly in cities where prices are highest. Corporations aren't "just scapegoats" here either - they are parasitizing cash flow from workers here as well. Corporate profits is where the money in high housing prices ultimately goes.
There is a reason billionaires astroturf YIMBYism. It's precisely because it doesn't threaten their class interests. Housing is a basic necessity and should be guaranteed. But that would involve taxing corporate and billionaire assets to finance, and tackling the issue of economic parasitism head on.
For example- do you have a mortgage? Almost certainly in your name, you have to be very large to receive a mortgage as a corporation. If you're holding a property in an LLC but the mortgage in your name, that's classic piercing the corporate veil and will take an attorney about 10 minutes to shred that in court