There was actually a story in The Atlantic today talking to the author of a new book on just that subject. The short answer for the United States is that it has to do with professional jealousy and institutional inertia.

Dentistry, like surgery started out as a kind of manual labor job, whereas medicine has been a university-educated job for centuries. Over time, the distinction between physicians and surgeons has narrowed, but dentistry remained a separate sphere, with dentists eager to protect their newly-established expertise and prestige. Closer to the present, the two branches of medicine have developed separate infrastructures as far as coding and billing, which makes their integration quite difficult. Both groups, physicians and dentists, have also been vigorous opponents of rationalization and especially against a national health insurance system that would treat them more equally, fearing that they would lose money and autonomy.