> What is the typical proposal for how they plan to keep the population constant, after creating all that space?
Have other metropolitan areas do the same so there is no net migration.
> Is there any example of a density anywhere going on record that the metropolis in this local neck of the woods should somehow say no to more people, rather than building more?
There is a difference between refusing new people and having population growth as a goal. People exist, they have to live somewhere, increasing density increases the housing stock and gives them somewhere to live.
If one city is hostile to giving them somewhere to live and another isn't, people might move from the hostile place to the amiable place. But the solution to this is obviously to make the other city less hostile, not to make sure that all cities are maximally hostile.
Have other metropolitan areas do the same so there is no net migration.
> Is there any example of a density anywhere going on record that the metropolis in this local neck of the woods should somehow say no to more people, rather than building more?
There is a difference between refusing new people and having population growth as a goal. People exist, they have to live somewhere, increasing density increases the housing stock and gives them somewhere to live.
If one city is hostile to giving them somewhere to live and another isn't, people might move from the hostile place to the amiable place. But the solution to this is obviously to make the other city less hostile, not to make sure that all cities are maximally hostile.