Gut feelings, discretion and perception together have another name, by which the founders called this type of law enforcement: “arbitrary” - the opposite of lawfulness.
A law enforcement officer must be bound by the law. By substituting other elements for explicit authorization in law, we depart from a system of law and justice and end up with something else, something in which you or I have no rights or liberties worth the name.
The common law in force during our founding held that fleeing felons could be killed. So go lecture our founders.
I think they actually believe in their little "Tag - You're Dead!!!" police game.
Apparently, if a policeman touches my arm, and I shrug his hand off, I've become an INSTANT FELON, and can be killed out of hand - just as the Founding Fathers envisioned...