Einstein competed against all the other scientist that were trying to come up with a theory to explain the different aspects of physics. Academia is one of the most competitive areas in our society. Da vinci was competing to be the best in his field. He operated in a broad range of areas but his focus was in the Arts. His goal was to be the best relative to his peers. Again competition with his peers moved his efforts forward. High level talent does not exists in a vacuum. It's only the best relative to the others which is a competition to be the best.
In a perfect world collaboration would be ideal but we have seen that people just stop trying after awhile and become free riders with only a few doing the majority of work. So in affect collaboration wastes a lot of potential effort by letting people ride it out.
Long term competition is the best way to move forward but it can't be the all out version where resources are wasted rather than used wisely where we try to win at what ever cost.