I can't prove that they're not happy, but I think you'd have a really hard time proving that they're happy as can be, and you made the assertion. I do no think that the west really has to worry about less developed nations (I personally hate the term 3rd world) rising up against them and demanding their fair share. The west has too many resources (often times taken from these countries) and technology that these nations cannot compete with. These nations also are often times rife with crime, unless there is some form of totalitarian regime in charge that controls the population and deals heavy punishment to criminals who go against the systematic crime-structure in place. Crime often times comes from a place of social/economic inequality. That's not to say all crime, but a good portion of it. When people can't get what they need, they'll take it from others. As long as these nations are deprived of their needs and access to their own resources to use for their own purposes, there will be civil wars. As long as there is inequality, like I said, there will be physical conflict. Of course, a regime of complete centralized power could come in to play and suppress its citizens. This might not be a war in the technical terms, but it is armed aggression, either through fear or actual implementation, against the populace.
I agree that crime arises from desperation and poor socioeconomic conditions, but crime isn't exactly the same as war... even coups and violent revolutions tend to be more contained than wars. If someone is being kept down, then they're usually too weak to do anything about it.
The worst wars have always been between strong global powers/superpowers-- the European Wars, the World Wars... and then of course, the cold war-- a nuclear war between USA versus Russia would have been absolutely cataclysmic in the 80s, but as a comparison the war in Iraq, which is certainly a mismatch, is relatively contained and has a much much lower casualty rate.
I'm actually more likely to believe that if global equality were ever achieved, it would mean
more wars, and probably more horrible ones. It would be nice at first because everyone would be so happy, but then a few generations later that act of kindness would be forgotten and people would start asking themselves if they could get more, or why they should settle for what they have... and there would still be corruption and envy and need and desire.
Like it or not, the power imbalance is probably a good thing in terms of limiting the scale of conflict. In fact, the centralized world government that everyone is so terrified of is probably the best shot at bringing total peace to the world... no equality, but peace.
I also think that for the most part, weaker powers do not attack stronger ones unless they're insane... if everyone was the same, then all it would take is a single dispute and then alliances would be forming and you'd have an enormous war with huge amounts of people being killed.
