No, @Bill1939, I didn’t (and don’t) reflexively reject your final point – which did actually make perfect sense – because I was put off by because competition requires the separation of self (including an extension of self to a group) from others, it encourages the importance of one’s ego and diminishes the possibility of recognizing their connection with anything outside of self which did (and does) seem to be a load of codswallop.
Competition occurs on many levels: individual, as you seem to be fixated upon; partnerships, teams, families and other chosen groups, and geographic / national groupings. In the Hobbesian world which you seem to imagine Rand promotes, there would be zero opportunity for altruism. Among human groups (and even some of what we refer to as “the lower orders”, including insects), competition is what has driven the improvements in our world. You sit around the campfire chanting Kumbaya, and I’ll be sharpening drills with my team, improving our profits, and later we can compare notes on which group made improvements in the world, whether consciously or not.
There is absolutely nothing wrong with “a little greed”. As with any human endeavor, a monomaniacal drive to “get all the things” would be destructive. You show me one person working on that kind of single-mined pursuit (for real, not just “Well, the Koch brothers, obviously!”), and I’ll show you a thousand working on the single-mined pursuit of “Sharing what belongs to someone else – for the common good.” (I’m not aware of any human monomania that has an overall good outcome – including altruism.)
Whether the idea appeals to you or not, and regardless of our inclusion in “the whole universe” and various subsets, we are each and all separate and we do best when we keep that in mind, instead of imagining that we’re part of some kind of collective.
To get back to the point of the question: Yes, “to an extent” competitive sports are good, to the degree that they spur improvement in ways that would not likely occur without such head-to-head or team-to-team manufactured “conflict”. (And when the competition involves fair play all around and does not evolve into “hatred of the other team”.) When kids start wearing different colors and killing each other for “wearing someone else’s color”, then obviously things have gotten perverted. And that’s my point.