It’s not always the people who are competitive. Many times, it’s the culture, the rewards system, and how employees are promoted.
Sure, your co-workers may be friends and do not like to compete. But if you are always being ranked, if your performances are explicitly or subtly compared, if promotions or rewards depend on rankings (or the dreaded bell curve), you will consciously or subconsciously compete with one another.
Competition is not always explicit. But, you can feel it when it’s there.
In order to create a truly cooperative workplace (or one that values “teamwork”), the rewards and promotions systems should be aligned with the culture that you want to create. Individual successes should be celebrated and rewarded (especially when individuals exhibit or live out the desired values), but not to the point of making individual success the top priority of an organization and its employees, whether explicitly or subtly.
Sure, competition can indeed grow organizations. But, cooperation grows organizations through genuine connections and networks.