I contend the problem is not manual flying skills per se, it is loss of situational awareness.
Understand where you are coming from, but the two issues are really inseparable.
Like many skills, operating an aircraft involves both cognitive and physical aspects. With sufficient practice and repetition, many of the required physical actions become wired into procedural memory and do not require much in the way of active thought thus freeing the mind to focus on higher order concerns. I once read that the best way to throw an athlete off their game was to force them to really
think about some basic skill (i.e. their golf swing, ball passing, foot work, etc). This would be enough to slow them down or force other errors. The same goes for pilots.
There is only so much that the brain can process at one time, so when additional neurons in active memory have to start thinking “okay, how do I physically execute this rarely used skill,” then those same neurons cannot be used to address the “what the heck is going on” question. In short, a lack of practice and/or training in manual (or otherwise degraded) flying modes denies the pilot the chance to fully incorporate these skills into procedural memory which then contributes to cognitive overload when that same pilot must then employ those skills AND try to diagnose an ambiguous malfunction.
As I have related previously, there was a time when simulator practice would include combinations of surprise, multiple (and sometimes ambiguous) malfunctions, with a generous amount of hand-flying. From a strictly bean-counter standpoint, this was a great deal of overtraining (i.e. more expensive) because, frankly, rarely do pilots find themselves in situations requiring this level of response. As a result, airlines (with the complicity of manufacturers) over time “streamlined” training into something that would probably cover most of the typical emergencies a pilot might face. Most, but not all.
There is simply no getting around the issue that the kind of training that would have helped the pilots survive these accidents, when applied globally, is going to cost a whole lot more money. The cynic in me says that airline managers are going to do the math, play the odds, and hope the next hull loss doesn’t happen on their watch.