Scott Adams anticipates their success:
My prediction that robots will dominate management before they dominate blue collar jobs is based on The Dilbert Principle which observes that the least skilled employees are promoted to management. You need your most skilled people doing interface design, engineering, and the hard stuff. Management is mostly about optimizing resource allocation, and that is something a robot can learn relatively easily, at least compared to most skilled jobs.
Another advantage: the robot manager "can be a hard-ass jerk as often as that is called for":
A robot might need to single out weak performers and let the rest of the team know who the problem is so peer pressure does its thing. A human couldn't get away with being so confrontational, but a robot has no feelings. It simply identifies inefficient parts of a system and highlights them. No one would bother wasting an hour of the robot's day crying in its office or complaining about fairness.