Yes they can, but only some. However, they cannot deny you the ability to profit off of your name and likeness. All streams of potential earnings by people are not equal under the law. Your name and likeness are protected by the 1st Amendment. Your analogy doesn't fit.
They can say "come play ball for us if you would like but if you don't want us to use your likeness then we will take someone else who will". It couldn't be any more simple than that.
