My 2 cents...
I handfly the plane until cruising altitude. Once straight and level, trimmed, etc. I engage the autopilot. A few exceptions though: when there's a lot of VFR traffic, if the SID is particularly tricky, or anytime a second pair of ears is more than welcome to deal with supersonic speech rate from ATC/unfamiliar accents/etc.
Brain resources are limited. Handflying is therefore only for the days when my CPU has a few cycles to spare... and the other guy next to me agrees!
Works fine for our type of operation but cannot suit everybody.