Birth control pills are prescription because they can increase the risk of a woman getting a blood clot. In the case of women who smoke, it's a drastic increase.

Sex-negative has nothing to do with it. Plan B is non-prescription.

Until very recently plan B was prescription only, so that's not a strong counter example.

The question is, does something about visiting a doctor to get a prescription for birth control mitigate the risk of a blood clot? Something that there would be no way to replicate with say better women's health education or a nice info-graphic next to the birth control section?

Condoms aren't prescription only in many jurisdictions either.