I used the Kansas war (between pro- and anti-slavery forces) to support my claim that a war between North and South was probably inevitable, regardless of whether the secession were allowed to proceed.
Indeed, the acceptance of secession would undoubtedly have made a western war much more likely, as there would be no means for a federal government to mediate violent disagreements between states.
The Southron aristocracy was perfectly willing to start a war to get their way in 1861. Suppose that they had been allowed to peacefully depart. The fun would've REALLY gotten underway after that. They would probably DEMAND territory from either the Western US, or from Mexico, on pain of war. The former would start a war between the Confederacy and the Union; the latter probably would have kicked off World War I some forty to fifty years ahead of schedule.