It really depends on the patient. Some people want to be seen by a specialist, and in my opinion, that’s perfectly fine. If the option is available to you, go for it. However, because hypothyroidism is such a common condition, it can very well be treated by a primary care provider.
Certain indications to see an endocrinologist if you have hypothyroidism would be:
People who are pregnant or trying to conceive
Any history of goiter or thyroid nodules
Uncontrolled symptoms
Not responding to levothyroxine
Health conditions that affect thyroid function such as a history of atrial fibrillation
History of thyroid cancer