Actually i think it would be the other way around, the more ports that need supplies the less is available. Yes, conquering towns that have/generate supplies is ofc best way to gain momentum. But on the other hand having more ports is also straining the total supply stacks your ports have/generate to keep them supplied. This can actually bring the regional capitols in on the chain with a better definition in the process. Keep a capitol cut off and slowly a string of surrounding ports are not able to be fully resupplying themselves or other regions because of the cut off.