If you are doing projection in just one dimension you can be assured to be wrong.
Here's another angle: In poor countries where farming is the main occupation, birth rates tend to be high. But as farming becomes automated, birth rates drop. Following this pattern, AI could push people out of service jobs and potentially impact birth rates in a similar way.
Of course this is just my mind making stuff up. Who know how it'll turn up.
This is a thread about the lack of people to work, not the excess. The jobs that are going to disappear will do so together with the retired/deceased workers.
(paid) hours worked per family are massively up over time despite exponential progress. We have stuff but no time nor security.
The countries with the most dire birth rates are the ones with a workaholic culture.
The depressing reality is rather than giving people back their time, even more of it will be pushed for in the future, to sustain the ageing population.