With airplanes there's a whole system in place to make sure that every airplane essentially gets its own private road. This simplifies the problem of automation immensely.
So maybe I'm wrong, but I don't see how autopilots couldn't be programmed to handle most kinds of failures (engine failure etc). Unless the failure is with the autopilot itself of course (which could have backup systems)
Most of the accidents with airplanes are caused by humans (https://www.boeing.com/commercial/aeromagazine/articles/qtr_...). So the real question is if automatic recovery would still be incapable of offsetting all the human errors.
For a prime example, see US Airways Flight 1549. The pilots Chesley "Sully" Sullenberger and Jeffrey Skiles intentionally disregarded part of the official procedure for handling a dual engine failure because they realized it wasn't suitable for their current situation.
FAA Part 121 flights are already so safe that trying to improve safety by taking humans out of the loop would be nonsensical. In some recent years literally more people in the US have died by falling out of bed than were killed in commercial aviation accidents.
Anything in an airplane is automated: takeoff, flying and landing. Pilots make mistakes all the time, but they still need to do things manually to keep their practice high.
People just do not want to go in an airplane without any pilots. In metro's it's not that obvious if someone is driving it or not. But airplanes, 'we' want a human pilot to be in control, else we feel unsafe. I think the same can be said about cars.