So it is hard to get that idea out of my head.
A seriously important problem! Training simply wrong from the beginning, then requires detraining at some future time, which is even more effort, and introduces more opportunity for damaging errors as skills must be learned. Train it correctly the first time! If the club instructors cannot train new pilots who can fly a safe approach at 1.3Vs, best replace or retrain those instructors!
Plus, what happens if the ASI is wrong ?
Ignore it! The 'plane does not know or care the indicated airspeed, it depends upon not exceed the critical AoA. Unlikely that the airplane is equipped to measure and indicate this, so you have to learn to feel what the controls are telling you. ALL light GA 'planes can be safely flown and landed by feel alone, by a pilot practiced in doing it. When I was checking out a new pilot in the Super Cub on skis two weeks ago, he asked me what approach speed to fly. I told him that I did not know, and just fly by feel. I think he did, and he flew very well. 'Best to learn to not need ASI....
We have too many instruments in 'planes anyway!