Corporations are able to do that because housing is a good investment.
Part of the reason it’s been a good investment is due to things like exclusive mcmansion zoning. Just imagine if it were easy to build net-new houses in those communities. Developers could make a killing building new housing, and extorting corporations into buying it.
There’s only so many people willing and able to pay sky high rents. At some price, people move into their parents basement, double up, become homeless, etc. So corporations have two options: either they continue to outbid average Joes or they don’t. If they don’t, then people won’t be forced to rent from them. If they do, at some point the new housing will just go vacant unless they lower prices.
Owning vacant housing has costs, but little upside. As a larger and larger percentage of their portfolio becomes vacant, housing becomes a worse and worse investment for them. At some point, it’s unsustainable, they have sell, the market collapses, and rent becomes cheap. They literally can’t sit on an unlimited amount of vacant housing and remain solvent.