To be considered safe, an auto-fly needs to be able to gracefully degrade as the subsystems in which it depends start to fail. Human pilots are trained to handle this by compensating for system failures in a variety of ways, including compensation (eg in a split flap scenario) and disabling (turning off a misbehaving autopilot). Ultimately, a human pilot can always turn off all the automation and fly the plane by looking out the window (or, in poor conditions, using gyro powered “steam” gauges).

In the case that the pilot is disabled, then auto-land is a great option, even though it’s reliant on so many subsystems. But for an always-on auto-fly, the requirement to gracefully degrade, and degrade, and degrade, and still operate at the level of a human pilot using the “Mark 1 eyeball” is a tough one which hasn’t yet been met (as far as I know).

There’s mention in this discussion of fully automated drones. But, those are basically expendable if there’s a serious system failure, since there are no souls on board.