Why would I want to rub my friend's faces?
It doesn't mean anything, it's just supposed to be a "cute" interaction. There's no benefit.
Nintendo seems to like that sort of thing, as it appears in games like Tomodachi Life as well.
It's just flair, there are no benefits for doing this.
Rubbing a face in Miitomo has no purpose, it is purely a visual effect to make the game feel more immersive.