People enjoy living in cities, at least some of us do. Personally the thought of everyone living on their own personal homestead manned by robots sounds really boring and lonely?
Anyways, there is nobody saying that you can not stay in a big city.
The core of the claim is that people on aggregate will not pay a city premium when it does not come with a job premium.
To your benefit: cities will likely become much cheaper! (and more filthy and crime ridden, but that's another talk).
However, what I think we will see is hyper agglomoration. We will likely see 2 or 3 mega cities where the last interesting jobs will remain along with basically all wealth.
These cities will be incredibly exclusive.
Likely one city in the US and one city in Asia somewhere.
The EU will likely be the big looser.