"Feeling" has nothing to do with the issue. Current autopilots are generally unable to cope with equipment failures. The pilots are primarily there to deal with unexpected failure modes.
Most of the failures have multiple backups, and most scenarios are also accounted for on how to handle them.
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)
It is impossible to program an autopilot to handle unexpected failure modes; there are essentially an infinite number of possible failures. Experienced human pilots can often figure out how to recover the situation based on applying fundamental principles. Computers won't be able to do that until we have something close to AGI.
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.
