dentist are tooth and mouth doctors. We know more about the teeth and mouth than anybody who just went to medical school and didn't specialize in those areas.

We do invasive surgeries and are licensed to prescribe controlled substances like physicians. Because we are doing invasive surgeries we need to be able to have an understanding of health conditions that could cause complications during procedures.

We also need to know enough to be able to prescribe medications that aren't going to cause problems in health conditions or with the other medications the patient is taking. We take many of the same classes the physicians take in medical school to get this foundational background.

Before patients recieve cancer treatment or transplants, they are required to have dental clearance from their dentist. Teeth aren't their own entity with no effect on the rest of the body.

Many dentists have hospital privileges and are licensed to do conscious sedation.

A physician has a much wider scope of knowledge, no doubt and earn their stripes doing an extra 3-4 years of residency. They have a much more demanding work schedule and have a much bigger responsibility. But refusing to acknowledge a dentist as a "type" of doctor is probably not fair. You could make some similar arguments for an optometrist.