Yes, there is continuity of abusive behavior in relationship. In general, close family members and dependent people gets to experience that most. Note that this is not exclusive to male abuse, female abuse exists too and is more likely to happen to dependents and family.

If you see sex as only proof of being accepted (as opposed to friendships and other social contacts), then I can see how it eases anxiety. It does not sound as if woman in question was important here.

If it is about physical aspect, prostitution sounds like fair way to solve it. If it is about philosophical or social aspect, making self worth less dependent on sex would help there.

The worth given by woman when having sex is however only illusion. Women deciding on having sex with you or not is not actually deciding on your worth. The range of reasons for sex varry quite a lot, from positive to negative, from emotional to practical or to physical or just routine. But actual decision making is not scoring of worth.