I usually fly, with my hands and eyes, the first thirty minutes of about half of all my departures. Frequently, F/O expects that I'll put on the autopilot after we are cleaned up. I just keep using my eyes and hands all the way to FL and then some. This is really where the crosscheck is learned. At Mach0.84 a one degree pitch change produces an 840 foot vertical either up or down. So to keep it smooth one must learn how to do changes less than a quarter of a degree. There are times when the ATC load becomes busy and the A/P is connected. But when not I keep my hands and eyes trained.
One the way back down, I'm again on the eyes and hand below ten thousand.
The auto throttle issue comes to fuel burn. I have yet to see a manual throttle pilot beat the auto system. The savings maybe small but ten kilos of fuel saved each hour by a fleet of 40 aircraft save the company money.