Medicaid and Medicare both exist. The question is not what to do with the poor or the elderly; that is (more or less) decided. The question is what would be sufficient for everyone else. If the public mandate is for catastrophic coverage, anything beyond that is a choice.
If someone who chooses no additional coverage wants birth control pills, they can pay for them or not get them. If someone with no additional coverage wants any other non-covered elective drug or procedure, the same answer applies. Private coverage should be allowed, just as all other private contracts are allowed.
Birth control pills save insurance plans money, making insurance premiums cheaper.
Births and congenital surgery are expensive.
Pills are made in factories and are cheap. Bangladesh offers free birth control pills.