Some experts believe that humans are, at best, only somewhat sentient, and only part of the time. Our mind automatically back-populates a story of thought and consideration before every decision, when in fact, our limbic system (more primitive, where our baser emotions come from) is pretty much running the show.
Many/most humans have the need to vigorously compete in groups. Again, some experts have compared this to troops of monkeys fighting over territory and/or dominance. This is still the case because while our neocortex has developed quite a bit, our emotional centers are still relatively primitive. At least, a lot more primitive than we're widely comfortable in admitting to.
I think that participation in sports is a necessary and mostly healthy outlet for these mental structures.
This can all come across as very high minded, and I don't mean to say that people who are into sports are more primitive than people who aren't.
I was never into sports, but I competed in different ways. And I've known people who were truly not competitive in any typical way, so it's complicated.
Also, the above paragraphs are loaded with simplifications and assumptions. (:
One way or another, I think organized sports are a useful and necessary thing for a large percentage of the human population. Of course, we as a society need to do it as 'well' as we can.