OP here. Why thickness should matter is precisely the question.

If you look at the treatment of this on Wikipedia or a physics text it is the phase difference beteween the front and back reflections which matter and not the total path length.

Even for a windowpane there will be some wavelengths where the two waves are in phase and others where they are out of phase. The true explanation is that for a windowpane these two kinds of wavelenghts are clustered densely together and therefore even for tiny wavelength ranges the interference effect averages out.