Why so few doctors are vaccine skeptics

Only a doctor who wishes to end their career (or has an independent naturopathic clinic) would come out as a vaccine skeptic. You may as well ask how many Monsanto executives think GMO's are a bad idea. Their investment in the current system is total, so they would be foolish to speak against it.

To speak intelligently on issues like this we need to understand incentive structures, just as John D. Rockefeller, the architect of the current medical industry model, did.

The system is set up to perpetuate itself, not to encourage independent thought. Those who speak up against it are either sidelined or their reputations (or lives) destroyed.  Not the sort of thing to encourage many to follow in their footsteps!