the Phantom wasn't a dogfighter....
They didn't need to dogfight, they had missiles. Of course when asked what else could be done to the Phantom to make it more successful the pilots said, "Give us a gun, PLEASE."
Secondly, it's been mentioned here that the Korean War produced the last dogfights of plane and pilot against comparable hostiles. I'd challenge that, as some dogfights happened over Vietnam.
They didn't need to dogfight, they had missiles. Of course when asked what else could be done to the Phantom to make it more successful the pilots said, "Give us a gun, PLEASE."