Tomahawk
Let's analyse what trim is for.
It's for removing the weight from the controls when the aircraft is at the appropriate attitude.
I don't know why your instructor did not teach you to trim on final and I won't try to second guess him.
Three points to bear in mind:
1 - when you remove power in the flare, the aircraft will start to decelerate and any sensible aircraft will pitch down to try and regain its trimmed airspeed.
2 - on most light singles, this pitch down is countered unconciously by the pilot and the control forces are light enough for this to be practical - however some heavier singles (e.g. PA32R) require trim to be added in the flare ro reduce the back pressure to manageable proportions; this is not an old wives tale, its in the POH
3 - if you sit on the flight deck of a jet or a jet sim and watch an autoland, the a/p in the models I've observed tends to slightly over trim nose up before the flare
Having said all of this, trying to fly the a/c using the trim instead of the yoke as a low hours pilot is not good and I could understand why an instructor may feel it better to encourage a pilot to develop a feel of the plane by using the yoke properly.
On training type aircraft this forces allow this, but as you have discovered the trim, used sensibly, is a wonderful aid!
Enjoy your flying.
