For anyone that has a legitimate diagnosis of.........whatever, and a Dr. wishes to prescribe Birth Control pill or some similar prescription, to deal with that diagnosis, I have no problem with that. (unless of course, its the mandating of a religious institution to provide it against their doctrine and counter the 1st amendment to the U.S. Constitution)
Otherwise, much of what you've posted as to "needs" are largely to lessen the issues of ...being a woman I guess. It's kinda like taking aspirin to lessen the risk of a heart attack. And as such, I have no problem either, if a woman chooses to purchase birth control, to lessen their risks of cancer, or uncomfortable periods, if that's what they have. But again, if they're having "painful periods", that indeed could be a medical issue, and warrants whatever the Dr believes can address that condition
Just wanting Birth Control to help prevent the possibility of a birth is NOT a medical condition or diagnosis that justifies ANY forced coverage of it by any insurance agency, much less a Religious organization