West Hawk
Obviously in RVSM airspace you have to fly on auto and to a certain extent you want to make the ride as smooth as possible so will use the autopilot.
Using the autopilot but monitoring it at all times still frees up brain capacity for other work especially in something like a jet which travels quickly.
Nevertheless on simpler departures we make it a habit of hand flying maybe up to FL280 and then engaging autopilot from there. It depends on the situation weather etc but its good practice to keep those hand flying skills honed.
flying mainly older generation Citations few have had totally reliable autopilots so you will tend to know its odd behaviour and be more aware than maybe a pilot flying a recent jet which is 100% relied on.
the same goes for small pistons you can get a Cirrus with an all singing and dancing array of pilot aids. There have been many who have used that aircraft capability to compensate for their own lack of skills and that is where the danger lies.
older varieties have everything from pure wing levellers to very unreliable behaviour and those require much more pilot intervention and monitoring
Pace