"if we have washing machines, what's going to happen to the servants whose job is to wash our dirty linen?"

I believe the demand for staffing will only grow as it becomes harder to find and evaluate the rapidly increasing specialization of knowledge workers brought on by innovations such as AI and robots.  

With robots, we'll be called upon less to provide 50 people to stack boxes, but we'll be asked to do whatever it takes to differentiate a standard full-stack developer from one who knows a particular library cold.

Nevertheless, it's fun to watch people freaking out over jobs as if robots weren't just another wave of innovation that alters the way we work.  Philippe Silberzahn got the humor just right with this sarcastic parody of robot-fear: