The type of problems found in competitive programming are closer to the sort of things scientists would be looking at, rather than your normal corporate coder. For example, placing lightning detectors to improve accuracy while minimising the number of detectors. This is something that you're unlikely to find in a normal business, but is fun to solve.
The grand idea is that competitive programming helps you view problems from different angles, to chase optimisations, and to practice application of algorithms and data structures.
Also, team programming challenges illustrate delegation of tasks based on strengths, and often require teamwork to solve difficult problems. This collaboration obviously carries over to general work.
Source: I was a competitive programmer in university
people are competitive, and competitions motivate. They aren't for everybody, but for some, they find it valuable. The competition and the coding ability are two separate life skills, forced together in the crucible of the high school education system.
I cannot criticize the motivation, or the fact that my students in high school can solve problems many professionals I know cannot. I can criticize that the competitive spirit marginalizes some of the groups we need to Encourage more.
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.