Is competitive behavior the worse human trait?

Evolutionarily speaking competition is healthy. It ensures that only the most fit survive. I'm not saying competition is always good, but did you ever think what would happen if we fully cooperated? There would probably be about 10 billion people, who would need to use more resources. I would be afraid if just anyone were allowed to, say, be a doctor. Without competition how do you know they are the best at what they do?