I agree with your sentiments Centaurus, and this appears to be a case of pilots letting the aircraft fly them, instead of flying the aircraft.
I'm sure the reason the autopilot would not engage was due to (pilot induced) control loading, but that is not the real point. The crew should have focused on recovery from the unusual attitude, rather than becoming obsessed with engaging the autopilot. As you inferred, there is a belief in the mind of some pilots that "the automatics will sort it all out".
I am sure you would agree that the recent policy change by Boeing to remove unusual attitude/upset recovery training from their simulator programs is a step in the wrong direction. What next, no assymetric training?
Regarding circuits flown on autopilot, if at night, circling in marginal conditions, I think that is wise, provided only basic modes are used.
Most airlines have a stated policy of no excessive FMS programming below 10,000 feet, yet this policy is rarely enforced.
In my view, if you cannot fly a circuit without relying on automatics, you should consider a different career.