It doesn't even take loosening population pressure. 1.6 birth rate in some country is only an average; some are still having 3+. If children start taking after their parents again, 1.6 birth rate now could mean 2.1 next generation and 2.9 after.

Also true, and whatever genetic component contributes to 'fecundity' will proliferate as those people have more children. Yet another mechanism that will cause populations to rebound. Fertility rates falling really seems like a short term problem, and we have plenty of those to worry about so it seems like it should be pretty low on the list of concerns.