Writing RPS is really the first step on the road to original writing, or at least a step further than FPS. FPS helps us future writers develop our style and become better writers, yes, but RPS helps us more.
Because good fanfic depends on taking someone else's characters and getting into their heads. But the groundwork has been laid for us already: there is such a thing as in and out of character, if they were written with any kind of consistency by their original creator. And why would we be interested in them if they weren't?
With RPS, on the other hand, we pretty much have free rein. Because yes, we're writing about real people, but none of us really knows what they're like. So we may extrapolate from things the celebrity in question has said or done in public, but ultimately what we're doing is inventing personalities, and putting famous people's names and faces on them.
So RPS is the best way to go if you want to write original fiction one day. It's practice.