[tropo]

This assumes uniform gene pools that never change. In other words, it denies evolution.

For each nation, he extrapolates various existing trends. This wouldn't be too bad if people within each nation were uniform. They are not. Given the choice between having children and having other luxury, people do not all make the same decision. The mental traits that influence this decision are inheritable, both genetically (brain structure and chemistry) and culturally (religion and more). It should be obvious that the portion of people who decide to have kids will increase. We'll be back to exponential growth until we hit real resource limits and start dying in squalor.

This is unavoidable. Anything done to stop it will be overcome, because those best at overcoming impediments to reproduction will come to dominate the gene pool.