I think you are in general right that agglomeration effects are real, which is why bigger cities have higher value to residents. I agree that people move locations. But I think you can go a step further. If one city is growing faster and densifying, surely those people are not demanding homes in other cities and those cities build slower. This is part of the spatial equilibrium story that further makes claims about “build density and get cheap homes” less plausible.
I think you are in general right that agglomeration effects are real, which is why bigger cities have higher value to residents. I agree that people move locations. But I think you can go a step further. If one city is growing faster and densifying, surely those people are not demanding homes in other cities and those cities build slower. This is part of the spatial equilibrium story that further makes claims about “build density and get cheap homes” less plausible.
My background: I used to work for property developers and have been researching housing supply for many years https://scholar.google.com.au/citations?user=P5s-_d0AAAAJ&hl=en&authuser=1