Years ago, when asked to write a TQ course for B737, I accomplished as much system demonstration and sign off as possible in the FBS phase. Of course some manoeuvres have to be signed off in FFS, but later on. FFS should be focused on handling and operating. Then, in FFS 1 I designed an aerial ballet of turns, climbs, descents, accelerations all mixed up, without FD's to educate the student how to control the a/c manually and learn the scan. ILS's & G/A's followed. This was very useful when converting from needles & dials to EFIS and Maps, and again when converting from up & over screens with ASI & VSI to the side by side screens with speed tape and VSI tape. This allowed 2 hours of acclimatisation and gaining fundamental knowledge of how this a/c wanted to fly. FFS 2 introduced some of the same with FD's. but only 1 hour. Then it was ILS's and G/A's, stalls etc. Now the student had full grasp of the basic a/c and the AFDS. FFS 3 moved onto SE work, a dedicated session. FFS 4 introduced the systems non-normals etc.
Since then I've had to teach courses where FFS 1 had a few moments of poling the a/c and then straight into complicated demos of systems non-normals and all with FD's. FFS 2 was a mixture of various QRH items and then 2 hours for SE intro. The students heads were exploding form doing 6 different QRH's in 1 session and then having to deal with SE intro when their basic a/c handling was still so-so. The foundations had not yet been built. I suggested a couple of extra FFS sessions at the beginning for more GH. Not allowed: "the students are paying and it'll make it too expensive; the course includes all the mandatory items and minimum hours and therefore extra is not necessary. If students are not to LST standard they can pay for extra training later on."
So there is the current philosophy. Sadly, they will not gain much manual flying on the line, as it is discouraged, and command times are 1/2 of what they used to be. Thus many commanders can not perform many basic piloting manoeuvres and there is no will to change. Without regulation and investment it ail get worse not better. Auto-systems will improve and pilots will indeed become button pushers and it will all go well and we shall all survive. There will be no incentive to have good GH pilots. Until............
Things will only change when a top politician or high profile person is the victim of a survivable scenario, but dies and then the questions will be asked: why did the pilot not save the day? Then something may happen.