I think you are exactly right, and in a healthy market that's what would happen. In practice, I believe we are so far from equilibrium that it would take such a long time for the trickle down effects to push housing costs in a range which is affordable for people that aren't well off.

Telling people that within 10-15 years if you keep building several hundreds of thousands of houses eventually rents will be affordable is not a winning slogan :)