If looting starving regions for food still allowed for the robbing of food (directly from the wealthy locals that aren't starving to death instead of the empty granaries), essentially allowing war to create food, it might serve as an incentive for realms to go to war to feed themselves. Though it's true that most of the time, when starving, one's reflex is to turn into a courtier and try to ease the stat drops rather than to march far away for a handful of bushels.
This would be an endless starving! In this case the 'try to ease the stats drops' will not work because you know all in the end is going to die!
The only way out would be to take the better 'grain' regions and try to defend them until the end... and loot grain from all your neighbours.
And if you give them a good reward, why would they giving up... Yes, in the end all nobles will left the island, but it's not the same leave it with nothing, than leave it with 50 scrolls, or 50.000 gold pieces... or any other reward!
PD. After said this, my personal opinion is to NOT close islands, but better the game and make it more fun, not smaller.
