Can't really reproduce history, though. We've yet to see the extent what humanity can do if they work as one, but most practical and theoretical fields are advanced by competition more than cooperation. Mathematics is a global competition between universities, chemistry is a race to make industry more efficient and profitable, biology requires patents and being first to market to be viable. Physics actually seems cooperative to me, but I'm sure the more practical sub-fields: electronics, structures, energy etc are all driven by competition.
My point is not about anecdotal examples. The ones you provided merely prove that mankind can withstand competition to some degree. My point is that you are making a statement which is likely supported by your vision and its bias, but not by any scientific study.
It is interesting to note that a conflicting opinion could be supported by the same logic and different anecdotes.
I'd say it was more technology that did it. Chimps both compete and cooperate and don't advance much. It was the invention of writing, printing, electricity and the like that changed things.