[dorfsmay]

As long at it is well documented and part of the training, and also ideally the system should indicate to the pilot why it is shutting down the engine(s), to avoid something like this:

https://en.wikipedia.org/wiki/TAM_Transportes_A%C3%A9reos_Re...

"The safety system automatically cut the power to the engine suffering the thrust reverser malfunction. There was no alarm in the cockpit to indicate that a thrust reverser had been accidentally deployed. The crew had no way of knowing what the true problem was. The copilot, seeing the right engine power lever automatically move to the closed position, thought that the lever had slipped back and pushed it back to the full power position alongside the left engine throttle lever. Once again, the automatic safety system closed the right engine throttle and the captain, who was conducting the takeoff, called for the autothrottle system to be switched off. After switching off the system, the copilot again pushed the right engine power lever fully forward and forcefully held it there."