Your missing the consumption piece. Unless they invent AI that will buy things on the late night shopping channel, AI will cause massive deflation.
The deflation may not be a bad thing - however it means our current economy can not continue. All fiat currencies will fail - they can't survive deflation. BMW will not need its robot. No one will be able to afford a BMW, nor will they have any job to drive it to. Maybe 1 BMW per block. We all take turns driving it.
I have no idea where this takes us - but clearly the current global structure will not be able to handle AI. We have seen other times like this in history. They tended to be very chaotic.
I agree, however the population will still be here. I'll say it again, I agree. (sometimes people take my posts in ways I dont mean them to be taken)
So everyone will still need cars and more free time will most likely mean more babies

so I think the population will stabilize.
But one thing for sure, what ever is going to be it will be. Meaning, the change is coming and I (or anyone else) have no idea what the future looks like but there is no stopping it and it is coming. Heck it has started, AI replacing humans at breakneck speeds. I think we forget, even a phone call to a company now I am clearly interacting with AI instead of a human in many cases. Heck they even give me credit for products I complain about.
I suspect these things will be addressed in a way that maybe supplements the population incomes. Such as some type of labor fee on robots that goes into a general fund. Yeah, I think chaotic is maybe the word because all countries are not going to be on the same page about what to do with humanoid robots working instead of people.
Maybe one day humans will be less expensive to hire than robots? Chances are wars will come of it too.
I wont be on this earth to see it, maybe that is a good thing? Maybe not.
One thing for sure, the countries that jump on the AI and robotic wagon will be the successful ones. Unless the world taxes those products differently from those countries....