Hard wiring with add a circuit

I have a simple question: If I want to hard wire my detector to my car's fuse box, and I have an add-a-circuit connector, why can I not simply use my old power cord, cut off the end that attaches to the cigarette lighter, strip the insulation, add a stakon connector to the ground wire and simply crimp the hot wire into the add-a-circuit? Why would I need to go an buy a new direct-connection line from the radar detector company?

Thanks for any help.