Isn't there some hunting safety rule about not shooting if you don't know what is beyond your intended target? After all, you don't know where your bullet may end up.
Wouldn't a person without peripheral vision be unable to fully evalute the safety of his shot? Would he be able to see another hunter near the deer? Then pheasant hunting should be allowed too.
You also mention right versus privilege. I agree, that gun ownership is a Constitutional right we have as Americans. But which ammendment gurantees a right to hunt?