I am a professional boxing writer who has to vote on who gets into the Boxing Hall of Fame so this question certainly resonates with me. With your mention of Harry Greb it is clear that you know your boxing because based on his record and opposition there are many of us who believe he is one of the greatest of all time. But is it legitimate to rank fighters from different eras-- or teams. Not if you imagine "legitimate" implies that there is some science behind it. But I think it is legitimate if you take your ratings with two grains of salt -- maybe 3. You look at a boxers overall ledger and whom he or she competed against. Fighters from the modern era such as Floyd Mayweather, will end their careers with 1/4 -1/3 the contests of a Sugar Ray Robinson - is it legitimate to compare them? Yes and no, but if no, it can be great fun. And perhaps from a Pragmatist vantage point that makes it legit. Thanks.
Not wrong at all, I'd say.
The only reason I can think of for thinking otherwise is that it would amount to not being loyal to one's country. We can agree that there are at least some kinds of loyalty we can normally expect from a good citizen. (Not committing treason is the most obvious example.) That said, it would be very bad if the demands of loyalty went all the way to which side you root for in a sporting match. That would be well down the road to mindless jingoism.
In one way it's a small point, but it has some real-life relevance. Noisy, thoughtless accusations of being "unpatriotic" are a far-too-familiar part of political discourse. If we worry that rooting for another country in a soccer match crosses the line, then the worry that we shouldn't disagree with any of our country's policies will seem all too real. That, however, is a disaster for thoughtful citizenship.
So root for the team of your choice. Root for them because they're the underdog, or because you like the way they play, or because you like the color of their jerseys. It is, after all, just a game. And you are, after all, not just a citizen of the United States but also of the world.
Sean has correctly pointed out that part of what you are asking calls for empirical answers. But your last sentence - about sports being the least thing humans ace invented - raises an issue of value. And what you seem to be saying is that since sports produce no tangible outcome, in your words, it's hard to see what their value could be.
I'd like to suggest that this isn't the best way to look at the matter. After all, why are activities that produce tangible results (making shoes, or painting pictures, or building houses) valuable? The plausible answer is that they contribute in some way or another to human welfare, happiness, or flourishing. Some things we need for basic survival - food for example. But a flourishing life calls for a lot more than mere survival. And if something is a reliable source of otherwise harmless pleasure, that pretty clearly gives it value.
I suggest that this gives us at least part of the answer to your question. Playing sports gives many people a great deal of complex enjoyment. (Exercises of skill tend to do that, or so the psychologists tell us.) But watching sports also provides people with a good deal of pleasure - as do listening to music, looking at paintings, and a great many other activities.
Not everyone enjoys sports, but that doesn't take away from the point. After all, not everyone appreciates Beethoven. And the fact that sports are reliable sources of pleasure need by no means be the end of the story. But I'd suggest it goes a long way towards taking the mystery out of the value question.