Yes, competition in and of itself can definitely be helpful in a variety of situations, such as making advancements—I totally agree with that.
What I'm not on board with is a competition to be the "best" country in the world overall (whatever that actually means…). What's the world benefit of one country being grossly superior to others? I only see that attitude/view causing problems. People can't choose where they're born, so what about all of the humans living in the other countries in the world?
Picture a classroom of 20 kids, where one child thinks he/she is better than everyone else and makes it known. Compare that to a classroom of the same size, where the kids recognize each one of them has their own strengths, weaknesses and quirks—but no child thinks they're "the greatest." In which classroom do you predict kids would get along better to work together and solve problems? In which classroom may cliques and problems arise?
That's just a quick idea that came to mind—I haven't fleshed it out, but maybe that comparison will help to better illustrate what I'm trying to articulate! :)