Many of the world's problems could be greatly alleviated if we collectively agreed that shrinking, not growing, our populations over time is the right thing to do. Unfortunately, nationalism incentivizes the opposite. No country's going to go first.
If a country wanted to have a shrinking population, it would likely want a fertility rate of just below 2. Japan has 1.41 (!) and barely any immigration.
The solution to global population issues is making sure that poor countries with high fertility rate (4-7) are brought down to 2-2.5, something which is already happening very quickly. See e.g. Hans Rosling's famous talks: https://www.youtube.com/watch?v=GeXJnOE-1gw
The solution to the low fertility rate is likely hard to change short term (cultural), but comparing countries in europe for example, it seems likely that making children reforms such as subsidized day-care, free higher education etc. would help.
So, what you propose is basic "you third world guys should be shrinking, not growing".
On the other hand, this first world countries, not the populous third world ones, consume most of resources and fuck the environment more...
That said, I = P * A * T holds. Environmental impact is a function of population, per-capita affluence (resource consumption), and technology.
Apparently one is.