Gertrude, would that be a Tiger Moth?
No, I just got the impression that if you didn't maintain your 152 or whatever properly then the rubber would go off after a few decades, and if you didn't replace it when necessary then the throttle friction wouldn't work as advertised. Of course the instructor who told me this was at pains to point out that their 152s got fixed when necessary, but that it was still a good idea to keep one's hand on the throttle against the day when one was flying some crappy aircraft rented from elsewhere. (Or, of course, against the day when one forgot to adjust it properly.)
In a 152, of course, one can adjust the trim without noticeably removing one's hand from the throttle anyway; I was certainly never taught to fly out of trim for more than a few seconds at any point[1], and I've been left with the habit of keeping in trim from wheels leaving the ground onwards.
[1] Except in a Super Cub on floats on final, that is. If you trim for final, then pulling the stick fully back once you're on the water isn't necessarily enough to stop the front of the floats digging in. So you're pushing forwards quite hard on final, feels very odd.