and it is my way of thinking not an official answer! It is a question of role. The constant force controls the energy which will power the escapement in order to make this flow of energy as stable as possible; it acts downstream. The behaviour of the escapement is obviously influenced but not by itself. The constant escapement acts on the escapement itself which in a theorical point of view is more efficient for the accuracy of the watch since even in a case of an instability of the energy, it can reduce this impact and preserve the isochronism.
Thanks for your comments!
Fx