First of all, they have a specific sport as a specialization of Athletics because
many sports do use Athletics. In baseball, it comes into play in a major way when running the bases, trying to steal a base, and catching a ball. In no way does it make it the only skill used anymore than Edged Weapons (Knives) is used to throw a knife. But according to you, since Knives is a specializatino of Edged Weapons, that's the only skill you need.
Second, Shadowbeat is a 1st Edition sourcebook.
Third, according to your take, sports found in Shadowbeat such as Combat Biking would only use Athletics, too. Bikes? No need according to you. Shotguns? No need. Clubs? No need. Whips? No need. Polearms? No need. And since Urbal Brawl is a sport, you wouldn't ever need to have any other skill at all, as it's basically Shadowrun-made-commercial. Unfortunately, they don't list stats for any athletes in there, nor do they ever say that Athletics is the only skill used.
Four, even if they did, 1st and 2nd Edition had a completely different style of skill system than 3rd Edition. Firearms, for instance, covered *every* firearm; pistols, SMGs, assault rifles, and etc. They also didn't have Complimentary Skills as far as I know, and they definately didn't have Knowledge Skills.
Fifth, and once again, 3rd Edition does specifically address Baseball. It's a use of Throwing Weapons skill. Whether you want to accept it or not, it's a canonical fact now.
Sixth, what skills would a ball player need? Athletics and Clubs are the two major ones, with Thrown Weapons being only average-to-good for everyone but the pitcher. They'd then have a few Knowledge Skills pertaining to their particular specialty. But you're right, that's silly. Only people with the occupation of "Shadowrunner" should ever need more than one skill on their job.
Seventh, some sports truly do rely much more heavily on Athletics than any other skill, such as many Track & Field events. Shotputting would not be one of them, but Sprinting and High Jumping would.
Eighth, as mentioned above, a professional pitcher (or hitter with Clubs) who spends exactly the same amount of Karma on Throwing Weapons (Baseball) is going to be a superior pitcher compared to a generalist in Throwing Weapons. By almost about 50% better. Yet the generalist is still going to throw knives, hatchets, and spears much better than the pitcher. That's how Shadowrun's skill system works.