Ready for the flaming, but here is my version:
Wife unilaterally enforces celibacy one month after conception of the last child.
Other woman is initially happy that the man being besotted with his child(ren) means that she can leave the the relationship if the novelty wanes, but he is unlikely turn up on her doorstep with a suitcase.
Does the wife know? Maybe, maybe not. He is supportive, pays the bills, provides.
Are there consequences? Absolutely, in my case the other woman wanted me to live with her - which was appealing - but on competitive terms that would have 'punished' the wife and child(ren) for losing. Unless you are extremely selfish (I have seen some) there is a guilt that one has to bear that can only be shared with two or three carefully chosen people at most.
Decades later, I am still supportive, pay all the bills and provide for the family. No sex inside or outside the relationship for nearly twenty years, but daily access to my child(ren) over that time.
I neither want nor expect any sympathy, but my advice to anyone embarking on a long-term relationship - shameful or not - is that they should outline their wants, needs and expectations at the outset, review them at regular intervals and assert their right to considerate treatment from their partner.