Strygil "That said, to conduct a relationship on the basis that "he wants sex, I don't, and he puts up with going without" is, bluntly put, exploitative, manipulative and bullying."
It's not bullying not to have sex with someone. No one has a right to demand sex. If a couple are not happy about how much sex they are having they should talk about it and decide how to proceed and that may mean proceeding to the doctor (if they think this is relevant) or to proceed in their direction away from the relationship.
I'd never advise anyone to stay in an unhappy marriage. Just to take steps to make it happier or, if appropriate, to leave.
"I can imagine only too clearly the outrage which would result from someone posting that their male partners refused to meet their sexual needs on a systematic basis. "He's shagging his secretary, he's gay, he's projecting his sexual inadequacy on to you, he's bullying you, yada yada yada".
There was such a thread on here, and the problem was possibly medical and the man would not seek help. And the posters advised the OP to do what was right for them. As I would advise the OP her to do so too.
The difference is the OP has a new baby and that baby will grow and things may change.