If you take the politics and religion out of it (aka. you move outside of the USA) then some oral contraceptives require a prescription and some don't. Preventing pregnancy is quite easy -- screw with pretty much anything hormonal and you'll dramatically decrease the odds -- but doing that without causing unpleasant or dangerous side effects is much harder. Some formulations have had enough testing that we can say that they are generally safe; others should only be prescribed after a physician has ruled out certain risk factors.
The dangerous bit in this case is that there are many formulations which fall into the category of "generally safe, but if you experience X, Y, or Z then you should see a doctor" due to rare but dangerous side effects. In such cases there's no need to consult a physician before taking the drugs; but they should not be given to a patient who is "not comfortable visiting a doctor" and would not obtain medical care if such complications arose.
There are plenty of patients who are "not comfortable visiting a doctor" to get birth control, but who would certainly obtain medical care if complications arose.
Some doctors require a full pelvic and breast exam for birth control prescriptions. Patients who've previously been sexually assaulted can be very uncomfortable being touched naked by anyone other than a chosen and trusted partner, but still accept the need to be treated for complications. Exam-less options are a godsend for anyone who cannot handle their first experience being with a speculum, or who need more time working through trust or intimacy issues.
The dangerous bit in this case is that there are many formulations which fall into the category of "generally safe, but if you experience X, Y, or Z then you should see a doctor" due to rare but dangerous side effects. In such cases there's no need to consult a physician before taking the drugs; but they should not be given to a patient who is "not comfortable visiting a doctor" and would not obtain medical care if such complications arose.