Why do movies first start out as an R then do a PG-13?

I know that horror films first start out as an R. But then the directors spend like 10 times editing the language and cut out anything bloody or gory to make it PG-13. Why should you go to so much trouble. Just make it like it is. SOmetimes like Saw IV it's first NC-17 hen just cut it and make it R. I mean if they just make it a PG-13 it's not gonna be that good cuz it's not that scary. And if there was any nudity/ from the R one. And then just put it PG-13 and edit. I don't understand. Just stick with what you do I think. Don't change it!