I wish it worked that way, but from my nearly 20 years of urban land use policy study and writing, I have seen tons of evidence that it does not.

The problem is that the most in demand areas get new buildings at 4-6 stories, and then you get locked up - the airspace above them becomes unavailable for 50-100 years, when there was market demand for some taller buildings from the beginning. It's the same "push down and spread out" that causes sprawl, just more localized.