Sorry, just saw this. You're absolutely right about the etymology, but generally the suffix "-ity" in English serves to make an abstract noun out of an adjectiv

Sorry, just saw this. You're absolutely right about the etymology, but generally the suffix "-ity" in English serves to make an abstract noun out of an adjective. So it seems more likely to me that "facility" is derived from the English "facile" than developing alongside it. All that said, its just speculation, and facultas->facility/facilitas->facile would explain the subtle difference in meaning.