AEB braking was originally designed to not prevent a crash, but to slow the car when a unavoidable crash was detected.
It's since gotten better and can also prevent crashes now, but slowing the speed of the crash was the original important piece. It's a lot easier to predict an unavoidable crash, than to detect a potential crash and stop in time.
Insurance companies offer a discount for having any type of AEB as even just slowing will reduce damages and their cost out of pocket.
Not all AEB systems are created equal though.
Maybe disengaging AP if an unavoidable crash is detected triggers the AEB system? Like maybe for AEB to take over which should always be running, AP has to be off?