While I agree that nonmonogamy doesn't solve the problem of heterosexual members of gender A having almost sex almost exclusively with a small group drawn from gender B, I think it can be helpful in ameliorating a different aspect of the problem of loneliness, and in particular sexual loneliness.
If you're in a monogamous relationship with someone with a permanent major sexual incompatibility with you, your options are to stay together (likely creating sexual loneliness for yourself and possibly both of you) or to break up and try to find a different partner (creating sexual loneliness for your ex-partner which may, depending on circumstances, last a long time). Non-monogamous relationships are a lot more flexible with this kind of thing: you can have sex with a different partner without blowing up the relationship that contains the sexual incompatibility.
By "major sexual incompatibilities" I mean to include things like impotence, vaginismus, vulvodynia, fetishes that are a turnoff to the other partner, same-gender couples where one partner is nearly heterosexual, opposite-gender couples where one partner is nearly homosexual, extreme mismatches in preferences of frequency of intercourse, serious illnesses interfering with sex, and some constellations of asexuality.
Of course some people have vulvodynia, or frustrated fetishes, or whatever, and both they and their monogamous partner have a satisfying sex life anyway. But, as you can easily imagine, these situations often do lead to big problems with sex, and I think monogamy tends to amplify that into big problems with intimacy and relationships. (But if you're in a monogamous relationship that's struggling with this, and you try to solve a problem like this by going non-monogamous, you're probably going to have an extremely hard time with it.)