The problem is that there is overshoot - when you watched half your siblings die young, you don't simply take the doctor's word for it that your kids are all going to grow up strong and healthy. It takes a few generations to adapt. During this period of time, you have excessive population growth, and then even if these people have children only at replacement rate, the population will still increase as the more populous younger cohorts replace the smaller previous cohorts.

Eventually people start having sub replacement rate children as there are just too many people. In theory this is good, but soo too here will there be overshoot. If you were an only child and your parents were only children, it's hard to start having large families. Even if you wanted to, you need to support a lot of older generations, which puts a severe strain on your ability to also have lots of kids. Eventually yes, things will turn around and the population won't go to zero, but decades of population shrinking and the associated economic issues will do a number on the population. India will have to deal with this problem in a century, much of the developed world will have to deal with it a lot sooner.

https://www.sciencedirect.com/science/article/pii/S109051381...

The heritability of fertility makes world population stabilization unlikely