I disagree. I think much of human suffering due to competition stems from lack of security, or the lack of reassurance that basic needs will be met.
Imagine a technological utopia. All of your needs as a human being are met. All of the needs of your friends and family are met. Can you not imagine how much easier it would be to advance toward a "social utopia"?
Before the Renaissance, the cut-throat psychotic human beings tended to do the best in terms of gathering resources, security, etc. Since the Renaissance, this has become less and less true and merit has started to take precedence.
Eventually, once the conditions for a technological utopia are met and for the majority of the population, it will be a like a light has suddenly been turned on. Those that have all of their basic needs met, tend to be nicer to others on the whole.
Besides, even if I'm wrong, it's not hard to imagine some sort of machine or system that short-circuits "our biologically driven urge to dominate the gene pool" for the good of humanity.