If I had to guess it's because JD is more of a general physician. Strange was a neurosurgeon before the accident that crippled his hands and led him to study the Mystic Arts. So not only can he not perform surgery anymore without magic but if he was working on you, then you were pretty much in life or death territory anyway.

Not to mention less formal training than Dr. Quinn? At least he’s studied modern medicine and has specialty years after surgery residency.

Dr. Strange had his injury in 1963, he probably went through medical school in the 1950's and has been studying magic, not medicine ever since. His techniques and knowledge are extremely out of date.

Probably the same reason Zoidberg is considered to be on the same level of medical competence as Dr. Dre (Zoidberg literally doesn't know human anatomy), and a higher one than Dr. Pepper (Which is genuinely responsible for less death than Zoidberg is), and Dr. Evil (Went to Evil Medical School)

And even then all of these people are probably better doctors than Doc, the dwarf who lived back in the days when washing your hands was considered a "Rookie mistake no self-respecting gentleman in the medical profession would ever make"

And the Medical Profession consisted of people wearing scary crow masks who just spread disease around and kill people, fully believing that disease was caused by not saying "Bless you" when someone sneezes