Robots and automation will exclude the need of uneducated labour. The current fertility rate is sustainable.
This is an educated guess though. I agree with you that it is likely. I also think governments need to prepare for a big part of the entire population that might not have a meaningful job to do. But so far robots and automation have not yet completely excluded this need. Far from it. We don't know for sure if or when this will happen either.
This will be a big challenge in the 21st century. People need meaningful occupation to thrive, so governments must find solutions to do this.
While technology, AI and automation are certainly going to have a huge effect on jobs, work and labor, I think eventually they will create just as much work as they replace. I think most jobs will require different skill sets, a large number of jobs will change and of course some jobs will be fully automated and no longer necessary. But like other major technological advancements in the past, this one will also create a significant number of jobs and occupations that didn't exist before. So I don't believe for one second that we are heading into a scenario where we will no longer need to work, I think that is way too far fetched a scenario.
For example, I don't see knowledge workers ,especially those whose jobs require soft skills like managing people, providing advisory services in complex non-routine fields, communication, negotiation and such, losing their work to automation. I think those kind of jobs are going to be affected by automation, and they'll have to adapt to a more data driven and digital economy, but we will always need knowledge workers.
So to go back to the point about aging populations needing immigration, I think that will still stand. But again, these countries need to focus on getting immigration right.