Securing National Integrity is the most basic purpose of government. If Lincoln didn't uphold Federal authority, the United States would cease to exist.

And you have a misunderstanding of the Strength of the Southern Economy, in 1860 the Southern states alone had the 4th largest GDP in the world. An Independent Confederate States with no war debt, fully functioning infrastructure and government would be in a powerful position to make trade agreements with other nations and secure loans. Something they successfully did during wartime and blockade