A lot of good answers have come up already, and mine are going to overlap somewhat.
1. Appearances. Many people are much more concerned about what the neighbours will think than they are about satisfying their own needs. Polyamory is not accepted by the mainstream. Sneaking around means you can still appear to be monogamous to the outside world. Ironically, there's also less stigma attached to being the "other woman" than there is to being in a consensual nonmonogamous relationship. Though frowned upon, cheating is basically accepted by our society. No one (except the wife) "blames" the Mistress, they blame the husband.
2. Cowgirl/Cowboy syndrome. I'll never understand how this is rational to some people, but there are those who like to date married people, break up the marriage, and steal the partner for their own. What I don't understand is how they fail to realize that someone who leaves a spouse for another partner is certain to repeat the pattern when someone else comes along.
3. Communication. Polyamory is hard. You have to talk about your feelings. Yuck. Who wants to do that? Our society has a "cheating culture" with predefined rules and expectations about how to have an affair. If the Other Woman is jealous of the wife, tough shit. Deal with it, or leave. A woman sleeping with a married man doesn't have to talk to him about her jealousy because she's expected not to feel it. She can just go ahead and bury those feelings. Not healthy of course, but "easier" for some people.
4. Commitment issues. Because she knows her role, and that the affair will never grow past a certain point, she doesn't have to make a commitment. She can keep the relationship at a maximum level of intimacy without having to give up too much of herself.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker