So you have attractive locations being completely dominated by rentable corporate owned housing and the net outcome is that people are completely boxed out of home ownership. There's no way pricing comes down because they do this in areas where people are willing to pay top dollar to live.
I live near Ann Arbor and we're seeing it play out right now--more dense housing in the inner core is being allowed (as current thinking says should be done) and whats happening is that smaller old-timey landlords and homeowners are being pushed out and their homes and apartment buildings are being replaced with brand new high dollar rentals. Not condos (although there are some of those as well, but fewer), rentals. And the rental prices are going up! Normal people get pushed further and further from the attractive areas to live, and pressure from these people moving out pushes up rent in the surrounding areas.