Edgar carried a big stick
Why hasn't Ramirez been assigned that role already? Or rather, why aren't players like Ramirez more often turned into DHs? Two reasons: One, most players prefer to play a real position, no matter how inept they might be in the field (we humans have a real talent for self-delusion). And two, once you turn a player into a DH, you've knocked down his value a few pegs. If you keep him, you don't have the DH slot available for some other good-hit, no-field player that comes along. And if you want to trade him, you've got to either a) find a trading partner in the American League, or b) somehow convince your National League friend that Joe Slugger's really not so bad at first base (no really, I swear).
So when we're looking for the greatest designated hitters, we really don't have a large group of great players from which to choose. Sure, Orlando Cepeda and Harmon Killebrew and a few other Hall of Famers finished their careers as designated hitters, but I don't think anybody wants to call Carl Yastrzemski a "designated hitter" to his face.