@Rwy in Sight, The autopilot won't sort out a bad situation, only the pilots can do that - hence there are two (supposedly) fully qualified pilots on every commercial flight above a certain size.
All the autopilot will do is fly the plane on a pre-defined trajectory. But engaging the autopilot in appropriate situations frees up brain space. Manually flying a plane, keeping to correct level, staying on a heading and speed, takes up a lot of concentration and brain power. If you are also trying to sort out a technical problem, or reset your Situational Awareness, then hand flying the plane as well is probably not the most sensible thing to do.
Put the A/P in, fly above MSA straight and level, or fly a holding pattern, while your PM sorts out the tech problem or your SA. Then continue.
The guy who spoke about Children of the Magenta was saying that Boeing pilots were using automation so much that they were getting very rusty at hand flying, and therefore would not hand fly unless they absolutely had to. This accelerated the rust accretion, and is a valid point. (The guy was old-school and seemed to be wary of automation and obviously preferred to hand fly when he couldn't work the automation, because hand flying is what he understood).
@vilas, regarding discontinuing the approach, you state how that should be done, but it is obvious that this crew were incompetent for whatever reason, so we cannot assume they would discontinue an approach in the correct sequence, or in fact do anything in the correct sequence.