But more importantly, if the Earth really is a rotating sphere, why do ANY calculations at all based on fiction?
Because it's easier and gives good-enough results. If you're dealing with gravity for example, Newton's work will do just fine for 90% of cases - but it'll break down when you have to deal with relativistic stuff and the like.
As an aside though, "it's not rocket science" is actually quite an annoying meme. When it comes to maths, rocket science is at the easy end of the spectrum. Think about it - for a trip from Earth to the Moon, you have far fewer variables to deal with than if you're dealing with aircraft. No air, gravity functions really simply, etc.