If you're offering up that analogy yourself, I guess I don't understand why you're asking, "what's the point of competitive programming?"

The point of "competitive _anything_" is The Competition itself. What's the point of competition running?!? Shouldn't running be a utilitarian function of escaping an angry lion in the African savanna? Therefore, what's the point of Usain Bolt competing in sprints?!? It's the competition. Same reasons for competitions in spelling (spelling bees), cooking (Iron Chef), etc. Humans just like to compete.

You don't have to enjoy those competitions to understand why other people participate in them.