I would assume "peace keeping" and a gradual expansion of Dominion Space, probably once every fifty years or so some planet gets the idea they can revolt. I'd also assume that they only breed as many as they need so each individual one gets more to do, it would also explain why the Dominion didn't interfere for the…

Since we're talking about baseball experience here's a fun bit of trivia, the actor who played Rom, Max Grodénchik was a semi-pro baseball player in high school and had to bat left handed to play as badly as he did in the episode.