Seems the same should be done for physicians. That would make it easy for the physician to prove his/her status.
My state does in fact issue such a card. So what? There's no need for me to carry it when I'm off to visit my grandbaby. And yes, the ground-based aviation folks could check a doc's credentials, as it is public information in most states -- but it takes time, not something to be done while CPR is contemplated.