Well written Tee Emm. You should do it for a living!
However, piloting and not prose is my profession and I put it to you that:
It is essential to maintain manual flying skills to a good level (well…sorta average for me – like most of us); but flying modern airliners in complex environments demands additional skills, especially if you want to look after yourself and thereby the customers. All of those skills have been mentioned in this thread. Manual flying skills can (should) be maintained in the simulator and down-route in appropriate circumstances. Time has taught me to be a little wary of those who need to augment their ego by demonstrating their superior manipulative skills.
Son, let me show you how I can torque turn this bird…SHEEIT!!...Holy Dooley that was close! Sorry, let me buy you a beer.
Son, let’s blast off and while we are turning and you are flying I’ll put us on the standbys and if you can’t handle that then you will have to learn how to fly.
Son, let me demonstrate how these birds can stall. Don’t worry about the edge of the sky being that close – I’ll pick it up.
Son, I have flown to Hagen a thousand times and I know that gap is just the other side of that piece of cloud. I’ll put her down just above the J and we’ll squeeze through – I can do it.
Son (in this case, maybe Yani), don’t worry about the AP and the published missed approach, I’ll just wheel it round and put us back on final.
...And the music goes on and on!
If you think you recognise any of the above situations and find my interpretations offensive, I apologise. Four of the above PICs are no longer with us; I regret deeply that they are not here to pass comment. Two were definitely superior “stick men” (I knew them well). The others thought they were better than your average bear; maybe they were, but they sure should have exercised some of those aforementioned other skills.
I believe the great majority of Captains, airline training departments and operational managements do encourage us to maintain our stick-and-rudder skills - IN THE APPROPRIATE CIRCUMSTANCES.