The crux of this is whether Us vs Them is instinctual or learned. I don't think we yet have a definitive answer, but certainly Us vs Them is so ingrained in our ways of life that removing it would be extraordinarily difficult.
Again, I may be excessively cynical, but my belief is that some people, maybe even most people, WILL take these mental pathways you describe no matter what, and the best we can do is provide distractions. Bread and circuses. At their best, these distractions channel our self-destructive tendencies into harmless oceans of impunity. At their worst, they are hijacked by ne'er-do-wells to transform the apathetic into frothing zealots of a cause they don't even care to understand. It becomes the responsibility of those who are paying attention to design a system that is resistant to abuse.
Presuming I am wrong, that means that there is a path for society to eliminate competitiveness from its apparent nature. I agree that would lead us toward utopia, but I am very skeptical such a path exists, and that those who attempt to follow it will simply be eaten by the wolves they believe they can train.