I always teach hand on the throttle below 1000'. Generally take off and landing. Had a student from another school that needed me to pull the power on him, on final and on take off, 8 or 9 times to make him put his hand on the throttle lever.
He had been taught, at a previous school, to never touch the throttle unless he was moving it !! He also pulled the mixture twice on me downwind, in my opinion because his hand wasn't familiar with the controls.