Speak for yourself. I am at least as good as State governments at judging the competence of doctors to treat me. I suspect a lot of people are like me. I particularly suspect that a lot of people who have considerable experience dealing with doctors who were "certified" by State medical boards are like me. The question is not just how good or bad individuals are at it, but whether States are even worse.
But even if many are like you, I am not saying States cannot publish information about which doctors they think are certified. I am just saying that patients and doctors should not be restricted by that. Patients who want to rely on their State to do it can of course do that. But patients who want to make use of other information should be allowed to, and doctors should be allowed to treat them if the patients choose, without facing legal penalties.