What you are missing is that corporate ownership makes it much easier to raise rent. It is very hard for 100 000 individual small time landlords to collectively raise rent in normal conditions (i.e., with no housing shortage). Many will lower rent to get their properties rented faster. But if you have a dozen or so large corporate owners it happens almost automatically.

This is very simple and well understood economics. If you lower the number of providers of a good or service they gain bargaining power.

Large corporations work very hard to make sure there is as large as possible number of providers of every item they buy and every service they use. But somehow when it comes to ordinary people, we are supposed to pretend it is a good thing. No, it is not a good thing.