Green Dinosaur,
IMHO, the main reason for keeping one's hand on the throttle is so that one can close it asap if necessary during the take-off.
During the climb it is true that a worn friction lock can result in the power reducing. However, unless you have fabulous noise cancelling headset equipment, any significant reduction is highlighted by a change in sound when flying an aircraft with fixed pitch prop.
If one was to teach no trimming below 300ft then would also have to teach that the gear should not be retracted below that height despite what effect that can have on performance. After all, it takes about the same time to move the gear leaver through a few centimetres as it does to move the trim wheel by the same or less.
Yes the aircraft trim should be set to the take-off position before take-off. However you may have noticed that while aircraft like the C172 have a single position for take-off trim, the loading can vary by more than a bit. If you don't believe me, ask your back seat pax to lean forward for a minute and see what that does to the trim setting during the cruise.
Thus unless that POH gives a specific setting for every position of the C of G, there is probably going to be some trim adjustment required shortly after take-off and more so if the C of G is near any of the extremes!
Regards,
DFC