> Which have an effect on fertility and death rate.
Yes, but given that they are unknowns you can't just extrapolate from the presently available data and call it a day.
> But that doesn't mean this prediction is useless.
It's an open door that the world population will stabilize at some point, it is also an open door that the speed with which the world population is increasing itself is reducing. It has to, simply because more affluent people will have fewer children because they are not looking at their children as their source of income when they are themselves unable to generate any. Children as a pension scheme is a very common thing still, but that is fortunately changing.
> And this is would not be due to "sensitivity to initial inputs".
To a degree it is: any error in the predictions for the next couple of years will result in a much larger error in the future, simply because of the fact that population increase is a non-linear affair to begin with, and that any med-tech development that causes people to live longer will also cause a large increase in the number of people alive at any one moment.
Compounded those two could have an enormous effect.
For reference, the world, 80 years ago, so just before WWII had only 2.2 billion people.