It's interesting to read other people's thoughts on this. I imagine the helpfulness or unhelpfulness of exposing the affair depends on the situation and people involved.
For example, in my husband's affair, when I was suspecting the affair he filed for divorce (how's that for a reaction to guilt!!! He figured it was okay to get involved with OW because he was "going to divorce me anyway".... yeah, he filed the week before he had sex with her!!!!).
When I learned her name and number and confronted her about it their relationship still continued. They were just angry at me and my husband became financially vindictive.
However, the OW was married... and when I finally figured out his work number I was able to let him know about the affair. That really did kill the whole thing. In some ways I'm sorry I didn't know her husband's number earlier to kill the whole thing off more quickly. But on the other hand, I did want the affair to "run it's full course" so my husband could experience the reality of it eventually running down.
Also, there was no way of knowing what her and her husband's reaction might be. She might have divorced her husband and hooked up with mine.
So really, it's a throw of the dice.
There is no arriving, ever. It is all a continual becoming.