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I wouldn't disagree with a lot of what you're saying; however, it changes the subject to what exactly is raw athletic ability? To me, it means strength, speed, agility. Those are the attributes that will give you an advantage at pretty much any sport hat requires "athletic ability." I don't consider guys like Tom Brady or Larry Bird to be athletic specimens. I also don't consider endurance to be associated with raw athletic ability unless it's something special, like a legit distance runner or something. The guys playing professional soccer have better cardio on average than most NFL players because of the way they're built, but NFL players could drop mass and develop that endurance way before any of these soccer players are matching the strength and explosiveness of most NFL players.
I like your criteria of saying athleticism attributes that give you an advantage at pretty much any sport that requires athletic ability -- I've never seen it put so usefully before.
However, I think you have to include coordination, balance, and timing -- and in fact, I'd argue that coordination and timing are usually more important than strength, speed or agility.
Of course you need some of all of them. Someone with no strength can't even stand-up, let alone do anything in most sports. Neither can someone with no coordination or balance (watch someone with MS for instance, a pretty horrible disease). But coordination and timing are what allow you to learn high level skills in the first place.
For my part, I look at Larry Bird and Tom Brady and see two guys who are among the most valuable players in two of the most athletic sports out there (NBA and NFL), mainly because of out of the world coordination -- they're genetic freaks, very few people could do what they did no matter how many hours and years they spent trying to develop that level of skill.
Endurance is an interesting one. I partly agree with what you're saying, in that its an attribute that is only noticed if its insufficient. If your gas tank is too small then it'll strongly degrade your performance in most sports, but there's little gain in having a gas tank that holds ten times more than what is needed. That's different than say speed or coordination, since having ten times more speed or coordination will allow you to become almost unbeatable in most sports. For instance, imagine a basketball player so fast he could dribble through the entire opposition before they could move to stop him, or a basketball player that could sink baskets 100% of the time from anywhere on the court.
I'm not sure that most NFL players could develop the cardio necessary for soccer without losing all their strength and explosiveness -- most offensive and defensive line players have very high fast twitch fiber counts and low slow twitch counts, and big bone structures. By the time they lost enough mass to get the endurance, they'd be no faster or stronger than anyone else, and I don't think many of them have particularly enhanced nervous systems (for the coordination to apply soccer skills in high level play).
But like I said, I really like your definition of athleticism -- the attributes that allow an athlete to do well in most sports. Though thinking about that, it also includes mental attributes (which most high level coaches seem to think are vital).
