I actually think you have more control moving your finger, except for maybe some final finishing strokes. The reason is, exactly what you say, because you are right handed, you can control that hand better. And this is the case with most guitarists. You probably could get used to moving the file as the main thing, but it's not necessary. What's important is the final result. Of course that's a subject in itself. But I think you have much more control, for the most part, moving your finger across a stably held file.