Well, I actually was keeping my right hand on the throttle the whole time. My previous CFI told me to keep my hands on the throttle. Then again, we were practicing maneuvers such as turns, straight and level, descents, climbs in no particular order.
My previous
Looks like you got cut off there.
Leaving a hand on the throttle at all times isn't necessary in most airplane. Having a hand on the throttle during critical times of flight when the throttle is not expected to be moved (say during a takeoff), is recommended.
Some call this "guarding" the throttle and many also recommend not holding on to it tightly in case of turbulence, rearward seat movement, etc. Also in larger aircraft the takeoff setting may not be "firewalled" so bumping it around by accident may be undesirable.
In something like a Cessna where firewalled is the likely position desired, I like to not hang on with fingers but place my hand flat behind the throttle after it's forward for takeoff. If I get personally bounced around or moved rearward by the ubiquitous Cessna seat track sillliness, I won't be going rearward pulling on the throttle to idle.
And of course any time you're actually needing to move it, you'll have ahold of it then, also.
What your instructor may have been teaching is that during maneuvering you need your hand up there to adjust as needed. Might as well keep it there.
In cruise with a properly working friction lock, you can treat that hand to a break so it can do things like tune radios, follow checklists, write down clearances, and generally be more useful than leaving it on the throttle.
You'll learn that the most likely cause of rearward throttle movement in life, is having a CFI on board who always asks this interesting question when they pull it to idle when you're not guarding it: "Engine seems to have died. Hmm."
As you start doing your emergency engine failure flow and checklist.