I would imagine the British would have been able to build a more formidable “passive” offense if they held the south along with New York City. It’s possible they could have allowed them to set up a strong blockade of French supplies, help thin the American forces in any one area (now having to defend the north, ports on the east, and area to the south. Speculating even further, it might have allowed the British forces to send some units west to come up and essentially surround the colonies (on land south, west, and north and by sea on the east coast). Anywhere the American troops decided to attach, the British could face them on several fronts and constrain their resources.