If not all, but major types of lawn mower robots are rotary mowers. I presume1 that reel mower is more efficient, and is said to leave a better lawn health and cut. So, why industry go to the other option?
1 - I'm assuming the efficiency, as electrical rotary mowers have at least 900W universal-motors or induction motors, and a manual reel mower is capable nearly the same cutting speed.