I think you may be right about the overall problem, but I'm not sure I agree that density is the solution.
People starting families don't just want a house, what they want is enough space. Mothers want a yard they can send the kids out into when they need a moments peace, closets to store everyone's junk, and bathrooms big enough to walk into while pregnant.
I think disaggregating populations into more medium and small cities would help keep costs down and give people more space.