Are airfoil profiles patented? If not, why?
There certainly are airfoils that are patented. Here is an example. Here is another airfoil by the famous aerodynamicist Richard Whitcomb. I think it is tricky in practice to obtain a patent in that you need to define the airfoil in a way that isn't so narrow as to be useless for protection. Just claiming a series of coordinates would provide very little protection as someone could make minor changes to avoid infringement.