For one thing, the game would have a lot more action. Hitters would have a field day. After all, a dog's strike zone is extremely small, although it varies from breed to breed. Chihuahuas would be walked automatically. Yes, pitchers would have to walk the dog.
Dogs are fast.
The first-base coach throws a stick, and the runner is off toward second base. The third-base coach pulls out a milk bone, and the runner steals third. Stealing home would be a problem. The other team would probably use a pit bull for catcher. So, the home team puts in a Doberman Pinscher pinch hitter.