OK some oldies were necessarily trained to cope with this but a lot of people today may have many other useful skills but they don't include tricky handling and before you know it a UA is off and running.
I've never seen a training program that didn't include unusual attitude recoveries and or jet upsets. I finished recurrent training at the end of last month, and it certainly included upset recoveries, and automated, as well as manually flown procedures.
During an approach into Kabul this month, a generator failed, and tripped off, taking that side of the split bus with it, as well as the essential bus. As it was going, the autopilot began react erratically, the control column began to vibrate and shake, and then the yoke began to rock back and forth with a high frequency vibration somewhat like an aileron buzz.
The quick solution was to disconnect the autopilot and handfly, while troubleshooting the problem using checklists and procedures.
The autopilot in the airplane I fly will drop from "command" to "manual," providing basic functions, during certain types of malfunctions. However, when in doubt, get rid of it and fall back to basic flying. It is, after all, something one should have mastered at the student pilot level.