I agree with
Stuck_in_an_ATR. Many pilots idea of "manual flying" is following the flight director in LNAV & VNAV with the autothrottle engaged. What's the point? A monkey could do that. Some airlines' SOPs make it difficult to do anything else in a realistic manner, though.
I generally stick the AP in after cleanup but if it's going to be a busy departure with lots of frequency and heading changes in a high-traffic environment, I bung it in at 200' so as to free up some capacity in the non-handler.
If they're smooth on the controls, I personally don't mind how much poling people do when sat next to me but many are fighting the aircraft all the time, even in calm air and it's a relief when the AP goes in and the "turbulence" stops...
AFAIK, there are no current airliners certified for AP engagment *before* liftoff, so everyone *has* to practice things like keeping on the centreline, stopping the upwind wind lifting in crosswinds, rotating at the right rate to the right attitude, etc. These are much more useful skills to exercise than pretending to be an autopilot higher up.