I think it is intuitive that the higher heel cups are in a functional foot orthotic devices the more it will stabilize.
This is yet another reason why custom foot orthotic devices should be made distinctively different in this regards for dress versus athletic shoes. Sure the dress shoes (smaller cut) will fit in the athletic shoe, but you may get better control of the foot by separately ordering an athletic cut. Athletic cut or style orthoses tend to be wider (so that they don't move around unnecessarily in the athletic shoe, and they tend to have more cushion and, of course, deeper heel cups. In another post, I will talk about the pros and cons of deeper heel cups.
KevinRoot Medical has there suggested heel cup heights with the Rx. I typically use 15 mm heel heights in dress shoes for women, 18 mm for dress shoes in men, 21 mm for standard athletic prescriptions, and 23-25 mm when you are inverting the heel some in athletic prescriptions. Remember if you have a patient with significant pronation you can add 2-3 mm medially to the heel cup and remove 2-3 mm laterally from the heel cup. The opposite would be true for supinators. Therefore, if you are ordering a standard athletic orthotic device for someone with excessive pronation you can use a 23 mm medial heel cup and 19 mm lateral heel cup. This principle designed by Dr Merton Root maintains the overall width of the heel cup area.