I believe that most of us, if not all, will agree that the airplane must be flown first. It's an age old saying being passed on by flight instructors for decades: Aviate, Navigate then Communicate. The power of simplicity...if only it could be easily perceived.
Fighter pilots do have a tendency to 'drive' planes more than flying them which is why some find their flying style with airliners a little reckless. There's a stark weight and maneuverability difference between a fighter and an airliner! But I think the boys from the transporter/heavy-lift category might be good with civilian jets.
There are pilots to let the AP handle things after 400 feet and there are some who take it by hand up to the first level portion of the DP or until they're in a stable climb. Usually, the latter are the better pilots qualitatively.