"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."

Yes, a 100,000-firm marketplace forces participants to be price takers.

Yes, a 1-firm marketplace allows the firm to arbitrarily raise rents.

Why do you think a dozen-firm marketplace "automatically" tends toward the latter?

A dozen seems like a pretty high number. Explicit OPEC-style cartels are illegal (I assume) under anti-trust law so we're talking about about some pretty implicit forms of collusion.