I don't think the kid even has to be confused about what the parent is doing. If a kid sees a parent on the phone all the time (reading), they want to imitate

I don't think the kid even has to be confused about what the parent is doing. If a kid sees a parent on the phone all the time (reading), they want to imitate being on the phone. The fact that the parent is reading is a second level distinction that matters less to young kids, especially when they can more easily imitate "using the phone" by playing games or watching videos.