An owner gets to play fantasy in real life, going to work at a park. If his dad had never bought the Knicks and the Rangers, Jim Dolan would just be an angry guy who used to own a cable company. Thus, a shipbuilder and Watergate bit player named George Steinbrenner could take over the Yankees and turn himself into The Boss.
By buying a team, an owner can reveal their inner winner - or make people forget how they made all that money in the first place. If you happen to have the billions it takes to acquire one, you presumably have a near-infinite number of ways to spend your money. To its owner, a sports team is more than just a plaything.