You're talking in the first paragraph about so-called "enlightened self-interest," a Pearsonian thesis if ever there was one. Theoretically, of course, you're right; when there is an alignment of interests, a common goal, actions can coincide in a win-win situation. The most obvious example I can think of is the Allied-Soviet alliance of 1942-45. But built into that very example is a dialectic of sorts...the convergence of interest was against someone else, and part of the alliance was a bully in his own right, by your own criteria.
The problem with your military analogy is that his buddies DO back him up, in the military arena, but not in the international arena. In fact, the strong can't even get it together to act in the latter case; witness Ethiopia, Manchuria, Iraq. What you're really saying is that if the past of least resistence leads to cooperation, cooperation works just fine. The trouble is that while a liberal trade regime seems in the interests of all, it's not. Not when BoogaBooga in Swatziland looks around and notices that HoogaBooga in Shitziland has lots of diamond mines and a weak army, and no one is really paying attention at the moment...