There's no reason to think things would stabilize but even if things roughly stabilize in terms of population there's problems.

When a certain region in a country gets a cluster of great companies or really any productive advantage you would want more buildings and people there. In a country with a growing population that would make most sense as you need to build houses regardless as there's more people entering the job market who need a home. In a country with a stagnant population for every home you build another needs to be abandoned. This is more expensive especially when this happens enough where a school in the 'abandoned town' closes and a new school should be made in the better town. You can see how the first is more efficient, you don't waste your fine buildings.