Yeah, this bothers me as well and it seems like a lot of other people have the same issue.
It just breaks the immersion drastically, the same goes for Nick for example.
I would be happy enough is Beth just releases the specific console command to set their companion-home status back to their original location(even if this doesn't make sense for other like Strong).
I usually don't like the kids in Fallout because they are mostly annoying but Nate standing there all alone in the middle of Diamond City and selling Newspapers doesn't feel right at all.