It seems that there is always a "good reason" not to hand fly. Although I agree that there are places and times to practice raw data flying, I realize that for some pilots it takes some effort to disconnect (click click A/P, click click A/T, FD's off) and there you go.
The location is not right (i.e London TMA), the weather is not good, the pilots are tired, the experience split between pilots is too big, company SOP's, etc...
The fact is: just do it. And make it mandatory for yourself once per day (if short haul),once per week (if long haul), up & down from ground to FL100.
Late into this thread, but after reading this load of tripe, I'm wondering which "big" airline you work for? (although something sounding similar to Mikey Air is probably where you reside)
It may surprise you sir, that the very things you suggest as being required and necessary..or to use your Nike inspired phrase "just do it" would put the collective arses of everyone where I work in a rather large sling thanks to the PCMIA card. Not only is manual flight frowned apon, it is actively discouraged and mandated against i.e. there are no practice approaches..FD off AT disconnected with 400 or so paying punters in the back.
Manual flight where it is appropriate and required, but the maximum use of automation at all times.
If this doesn't sit well with you then I would suggest you have failed to understand that there are plenty of operators where we might get 3-4 sectors a month, and the vast majority of landings are after 10 or more hours in the cruise, I for one won't be disconnecting until 1000' AGL or reciept of landing clearance anytime soon, my manual handling comes along once every 3 months in the sim.
Honestly...ego monsters indeed!