Longtimer
I totally agree with Lookleft and George Glass. The big difference is the background of the crews flying the aircraft. The 737 was not, before the boom in low cost travel, an entry level aircraft for pilots with limited experience. The first jet I flew had a fairly limited autopilot and no autothrottles, and the SOP was that if we used the A/P in climb or descent we disconnected it to level off, retrimmed and then re-engaged the autopilot. The next two types were better, but as a result of flying them by the time I got to fly the 737 classic it was second nature to have hands on the control column and thrust levers at the one to go call, and all the time below 10,000 feet, so you quickly recognised if something wasn’t going right. This was reinforced by the instructors on the type rating course who were very familiar with one of the historic incidents referenced further up this thread, as it had occurred at the airline where I was training, and we were told about it in detail.
Now it is not uncommon to fly with first officers ( I’m not saying it doesn’t apply to captains as well, I just don’t fly with them), who will let the aircraft do all sorts of things without bothering to guard the controls, even sometimes to the extent of letting it fly the approach with their hands in their laps. Reminding them of SOPs and the reasons that we guard the auto pilot / auto throttle shows they understand it, but the fact that they’re not bothering would indicate that Captains they fly with aren't bothering as well, so the chances are that when they get promoted they will pass this lack of monitoring on to the F/Os they fly with.
But I don’t think it’s about not about not being able to fly, it’s about not being properly trained and mentored because of the much shorter “apprenticeship” which they now serve before getting into a reasonable sized jet compared to what used to happen in the 1960s when the 737 classic was designed.