Academy Award category for best stunts

I watched the movie The Fall Guy yesterday, and it made me think about why these professional people doing the crazy stunts in all sorts of movies don't get at least one Oscar statue during the annual event? These are incredible people with fantastic skills and they would definitely deserve more attention. Why don't they get the attention?

Is it because the actors consider them a threat, because they will take the attention from the actors themselves? Or is it just that many think of those guys as stupid people with no brain just doing crazy things because they have no brain?

By the way, I really enjoyed the movie. I have read quite a lot of bad reviews of the movie, but I didn't care much. I looked forward to the movie and I really enjoyed watching it.