That doesn't seem to be true in Japan yet. Housing and land are relatively affordable and yet they maintain very low birth rates and most people choose to live in large urban areas instead of the country. What would be different about the West?
Japan's population peaked in 2009 at 128.5million:
https://www.populationpyramid.net/japan/2009/
And in 2021 its only 2% lower than that.
2009 fertility rate: 1.37
Today: 1.42
So, it is improving.
Cost of living is not the only reason why Western people don't have a lot of kids anymore. A lot of it is a change in values, Western people just don't idealize/value having a big family anymore.
However that natural feedback loop will be disconnected if Governments worldwide are permitted to import millions of people to replace the populations.