Factions happen. Political power struggles happen. Even coups happen.
It's quite rare for civil wars to happen, or for countries to dissolve. With a world country where there were no outside groups to go to for support or see as an example, it will become even rarer. "Not in a thousand years" sort of rare.
Conflict within a country which maintains superior capacity to violence than it's constituent groups is very different from war. That doesn't mean no one gets shot, but it means no one carves the land up with trenches and barrages the enemy with artillery for months on end. Real war is a particularly ugly beast and very few things are like it.