This lack or presence of ownership allows or disallows you from doing what exactly?
The lack of ownership of a sport allows a competing league to begin operation without having to first seek permission from the owner of the sport. This allows for competition among leagues.
The kids need to buy baseballs and bats.
From any of several competing equipment manufacturers. Only Blizzard can sell copies of StarCraft.
And if you play professionally you're going to sign on with an official team or you won't be professional.
In any of several competing leagues, not just the one endorsed by the owner of a sport.