Would you then support mandatory coverage for birth control in health care insurance plans? Would you support condom distribution in schools? Would you support a national sex Ed program?
No, no and no.
Old people don't need birth control because of their age induced sterility, so why should they buy a policy that includes it? Sodomy as well is non-procreative, homos don't need birth control either. Same with celibate individuals- why should groups of nuns or monks or incel individuals have to buy a policy that doesn't cover them. Further, some major religious groups including the Catholic Church are morally opposed to contraception.
Ditto for schools, a lot of students belong to religious faiths that do not sanction prophylactics.
As far as a national sex ed program, different Americans have different ideas about sex ed.