My thinking, and really this is the only thing that makes sense to me, is that the Disputed Lands are disputed precisely because they are extremely fertile and act as the bread-basket for the three city states, much like the rural areas around the Italian city-states fed the urban centers.
Control over the Disputed Lands means that (in addition to having your armies right outside your neighbors’ gates) you’ve got all of the food, whereas your rivals don’t, forcing them to spend precious cash on importing it, which means they’ve got less money to compete with you for more valuable trade commodities. The flip side is that cheaper grain for your own city means that there’s more demand in the domestic economy for non-essentials – which is great for the largely luxury-based import trade – and the city’s reliance on Westeros for staple crops goes down, which improves your trade balance with that region.