Let's say--hypothetically--that the U.S. President walked out into Times Square in broad daylight and shot a person to death unprovoked. Who would prosecute that crime?

If you can't (or won't) be prosecuted, why hide your crime?

Well, in this hypothetical case one may say: Just go out there and shoot the bastard if he is not prosecuted!

Isn't that what you proud Americans have your guns for?

New York State, due to the fact that murder is generally a state level charge and not a federal one. However, your broader point still stands.