Rubbish, who teaches that bs.
Oh I see, you are busy enough managing the speed so let's take out the autopilot as well just to increase the workload a little more.....

Rubbish.
Have you ever flown a classic 737 or a 727 before they invented Autothrottles? Yeah they used an Autopilot that had speed hold mode and then pushed and pulled the thrust levers as required.......wow what a novel idea!!
It's not hard folks.