I think it's a remnant from when doctors were part of the 'upper class' of the village (or even city), along with the priest, the school teacher, etc. Whereas today, in more educated circles at least in my observation, doctors are just body mechanics. They derive most of their status from their pay. (Much less so e.g. in the small town I'm from, where doctors are still respected just for being a doctor - but are paid less).
Edit to add: I'm not going to modify my comment above because that invalidates all the responses, but it seems like all responses are taking the wrong message from my post: I'm not making some sort of moral judgement on the work of doctors, what I'm saying is that doctors aren't any longer so special that they're part of the intellectual elite (and hence are consulted on topics being their expertise) just for being a doctor. Sure most doctors do work that's beneficial to many people, but so do teachers, and I don't think anyone is going to claim that teachers have high status in society (because of it, or at all).