To me it wouldn't... It's a breach fo trust and your marriage is a conncection of two people not more. So in honesty people may mask it working but i don't think deep down anyone is happy with someone they're in love with sneaking off to have sex and be intimate with someone else and then get back in bed with you at the end of the night.
It’s not easy, and it’s not for everyone, but open marriages do work for some people. It does require more effort to maintain the relationship than traditional marriages, though. That’s because extra-marital sex often leads to jealousy and competition, as well as isolation and feelings of insecurity. The way polyamorous couples deal with these issues is by being completely open and honest with each other about their sexual desires and experiences. They may seek approval from their spouse before having sexual contact with another, and they usually have rules about how much they do or don’t want to know about that contact after the fact.
Open marriages can work, if both partners agree on boundaries. |For example, a friend of mine has an agreement that its just sex and if any feelings develop then they should be honest about it. To me it seems bizarre, but they seem to be happy with it. They see everything like love, shared life goals as being exclusive to the two of them and the sex they share outside of marriage as exclusive. In other words, its kinda like a night out. Whoever they see is just for sex and they see it as separate from everything else