I think he was correct in his prediction about America becoming majorly divided and more people becoming disenfranchised. Whether it's due to competition or a combination of other factors, that's difficult to say.
We've also had different types of competition. The Cold War was a type of competition which some people claim we won. All wars are a competition. Then there is global competition among nations on an economic basis, as well as internal competition within America between corporations and other businesses. There's even competition among neighbors and family members - struggling to "keep up with the Joneses." We also have competition among different street gangs and criminal organizations.
There's also athletic competition, academic competition. Our legal system and political system are designed to be adversarial in nature.
But we also have a cooperative side. It could be reasonably argued that athletic competition (as an example) can build character and a sense of teamwork, which are vital in promoting cooperation. Even competitors have to sit down and cooperate once in a while.
I think that the trap that America has fallen into is that, ever since WW2 and all during the Cold War and up until today, our government has depended upon and needed strong unity among the body politic to be patriotic and supportive of American ideals in whatever endeavor we may have embarked upon. Even despite open challenges and confrontations during the 60s and 70s, we still managed to hold things together and keep most of the people content enough to maintain ourselves.
So, we may find ourselves at cross-purposes. We want everyone to be relatively content and "sustained" to some degree, and we also want a united, patriotic nation in support of American ideals and interventionism. But we also favor a system of cutthroat competition which has gotten ugly and which can leave a lot of people out in the cold.
We want a laissez-faire capitalist republic...and we want an empire spanning the globe. We wanted both, and we'll probably end up with neither.