If "self" is really a system of multiple separate but cooperating components, the illusion - or rather, the mental abstraction - could be there for it to operate in a way that is beneficial for its survival as a whole.

Simply put, if you stop believing that you're sentient, you stop existing as a single entity that has a "self". Your existence and your belief aren't cause and effect, though - they're literally the same thing, just expressed in different words.