I don't think even at the moment, anyone has to prove that they are in possession of contraception on. So no, don't think any pics will float around of shaved balls. They will just be the usual dickpics that are tinder anyway.
More importantly, men have it easy, and that may very well be a result of patriarchy. Once things are easy, no one would want to give an easy life up and assume that men just act a certain way.
I think contraception will not go beyond latex. Inserting gel anywhere except the a-hole will not propagate far as an idea for contraception.
I don't know, it seems like a super easy way to solve the accidental pregnancy issue and make sex more enjoyable. It's just probably more useful in monogamous relationships than in something more casual.