As said above, the conflict isn't so much about the TERRITORY but the RELICS in there. Any argument about how to properly handle the artifacts between the three nations would devolve into "no, MY country is best equipped to study these allagan artifacts" and no one really dies in the first place so it's also about keeping the GCs sharp in the case of an invasion. The Alliance isn't particularily expansionist and an army that isn't kept well trained regularily starts to go rusty, and I don't think anyone wants that in the case of the next garlean invasion.