I agree that relationships can have double standards and still work, but that's only when the double standard really reflects what both of them want.
If she has absolutely no interest in seeing anyone else, and it doesn't bother her for him to do so, and it would bother him for her to date, then there's no reason to force her out into the dating scene. But if that doesn't describe their situation, then it can be problematic.
They need to identify what they individually want and need, for themselves and from their primary partner. Start there.