they are already here. For many kinds of aerial photography and film work, UAVs are taking over fast. Pipeline/powerline inspection is just starting, but it'll happen quickly there, too.
It's mostly simple jobs like that for now (no passengers), unfortunately those are the typical jobs that a low-time beginner pilot would have started out with in the past.
UAVs won't take over the market from one year to another, it'll simply slowly become a mixed market over the next ten years. Companies might have a mixed fleet, new UAV operators are going to start up and compete.