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I write as a Southerner whose family (on both sides) fought for the Confederacy.
One must understand that the conflict was neither a civil war nor a war between the states. A civil war is a struggle to control the central power of the state. The struggle between Lenin and the Whites was a civil war, as was the conflict between Mao and the Nationalists. Jefferson Davis never wished to march on Washington and displace Lincoln.
Nor was the conflict a war between the states (or regions) as that implies that the central power of the nation is enervated to the point that it is incapable of acting. The best example - admittedly imperfect - I can think of is the struggle between the great nobles in Japan prior to the establishment of the Tokagowa Shoganate (pardon the spelling).
The war, first and last, was a war of secession. The cause of the war was the secession by the Southern states. The conflict between the regions (the states) was driven by the existence of slaves and the foolish and shortsighted demands by the South to impose indirectly the Peculiar Institution on the areas of the country that banned the practice.
You are correct to opine that most of the common citizens of the rest of the country cared nothing for slavery. It is very unlikely that they would have “declared war” on the South to abolish slavery. They would have tolerated slavery if it remained in the South. As Northerners would not tolerate slaves living among them, Southerners would have been wise to confine slavery to the areas where it existed as a historical fact.