Would painting chalkboard paint over my existing paint still work? Or would the paint need to be stripped for it to behave like a chalkboard? If this is the case, would chalkboard paint even protect my car at all?

First, the existing paint would not have to be stripped off the car.

 

Second, for any paint to stick to what's already on the car, it would have to be sanded lightly with 400 to 600 grit sandpaper, enough to take the shine off the existing paint, to allow the chalk board paint to have something to adhere to.

 

Third, that being the case, even if the chalk board paint was rubbed off, the metal would still be protected by the original, primer coat, base coat, and clear coats underneath.

 

Fourth, why would you want to do this anyway? A Subie deserves better!!!!!!! (tongue in cheek)