Griezmann is too small to play the number 9 role up front alone. He'd get bullied in the PL. He isn't a point of reference - doesn't play with his back to goal as well as someone like Benzema, Suarez or Lewandowski. Heck, even Costa is better due to his physicality.
He definitely isn't a pure no. 9. Always has support up front, either at Atletico or for France. Swapping Costa for Griezmann would be a very very bad idea.