It's not that simple. Will we manage at 8 billion but with double the amount of retirees to take care of?

We will likely see a decrease in population..we should be ok with 1-3 billion. In 1600, world population was 500 million. 3.5 billion in 1975. Fears of human extinction is unfounded. However an uninhabitable planet due to exponential consumption is a real risk for future populations. Better to be a healthy billion than a starving dying 15 billion strong species.

The problem is that we're already decreasing our population too fast in many developed countries. We can't go down as rapidly as we went up, or society will collapse.

Immigration should solve it. Increasing replacement rate of developed countries doesn’t mean that exponential population in developing countries will decline.

Which begs the questions: is the race to fulfill replacement rate in developed countries the real reason to incentivise child births?

It isn't, as the rates are near replacement, which should not be a problem. (And increased health span allows some older people to remain in workforce.)

However, retirement and social systems were designed during a boom and were inadequately funded.