This is a money decision IMO.
McCown is talented enough for someone to take a gamble on him as their starter, as such there is market demand for him in a greater capacity and more money than he would make here in Phoenix. He'd have to agree to take backup QB money to play here and he'd have to assume the backup QB position.
Put yourself in Josh's shoes. Yeah, you haven't been the greatest QB, but you've shown flashes of brilliance and you believe in yourself. He owes it to himself to be a starter if someone's willing to make him one, and he's definitely going to take that over a reduced role and reduced $ to hold a clipboard for the Cardinals.