Re-read the articles of secession. The prize was the American West.
Really? Then why no Southern claims to Nebraska? Montana and the Dakotas? They walked away from all that. All they really tried to claim was New Mexico and Arizona -- and perhaps Colorado, I'm a little iffy about that, whether Confederates were more interested in the territory or just raiding the mine shipments.
The horse's mouth said different:
“I can't let them go. Who would pay for the government?”
The prize was State’s rights as promised in the great debates leading to ratification of the Constitution. Conveniently forgotten by several contributors above.