..."doctors are the gatekeepers to prescription contraception"....
That seems to be the 'problem', as someone above pointed out. They are not 'gatekeepers' to condoms or other forms of conception control.  So it puts them in a position to 'judge someone else's conscience. Or respect the conscience of their patient.

'contraceptives' might not be 'medicine' but they seem to require 'prescriptions' by a doctor, and pregnancy does have many medical effects on the health of a woman.

While you, being a doctor, or your nurse wife, may not have the 'aptitude or intellectual grounding' – if that is your personal testimony – to deal with this issue, I expect many do, or think they do. Many other people do, also. It is something that involves them personally, after all.