If that is your policy; stick to it! I don't ask for ID, BUT the person picking up must be listed in our contract as a designated pick-up person. If the child is old enough, I would also ask them "Do you know this person?"
It seems silly, but aren't we better safe than sorry? I would HATE if I released the kiddo to someone I wasn't supposed to!!!
Oh, and if it was an emergency situation and the person who was picking up was NOT on my approved list; I would absolutely ask for ID.