For me personally, I consider that a benefit of polyamory more so than a motivation for polyamory. At the height of my relationship I drew great comfort and security that H had other loved in the event that anything ever happened to me or our relationship. And I felt like I had a source of strength for myself in B being there for me if something ever happened to H.
Also, while I would stress highly that communication always works best when it is between the involved parties, there was a great benefit to having someone else to sound off or "prediscuss" ideas with involving the other relationships. And a big benefit to having multiple approaches to probelm solving. A problem comes up and you get to pick a) This is the kind of problem I would like to hear H's advice/perspective on or b) This is the kind of problem I would like to hear B's advice/perspective on or c) both.