Well this is sorta true. If the South was worthless land from which no money was being put into the treasury, they would have kissed it goodbye and said "good riddance." However, it was the source from which most of the trade wealth came, and it was just too important economically to let it go.
Because of slaves, the South was producing a lot of money for the Union, and they weren't going to let it go without a fight.
Slavery was an indirect cause of the war. Money and power was the direct cause.
That explanation completely ignores the succession of Sectional Crises that precipitated the Civil War, all of which were rooted in the question of expanding slavery into new territories -- a subject about which both sides were demonstrably willing to fight.
The sectional issues would not have been resolved, even if Lincoln had permitted the secession to continue. For example, the Missouri Compromise of 1820 limited the expansion of slavery to territories below the Mason-Dixon Line. That was fine, to a point -- but eventually the Slave Territories below the M-D Line ran out of arable land. Clearly that was unsustainable from the perspective of the slave states: to expand their plantation system, they had to expand north of the Mason-Dixon Line. Meanwhile, north of the Line, the Free states were expanding westward into an agricultural gold-mine, and they weren't going to give that over to slave-holders.
And you also, of course, leave out the fact of slavery in and of itself. To defend the South on the terms the South itself defined, you're in the position of having to defend the continuation of slavery. There are no two ways about it.
From the perspective of the North, the abolition of slavery is easily justified as a matter of the same basic human rights that were laid out in the Declaration of Independence, and in the writings of the Founders themselves. It's an easy case to make, because it is a moral case.
As for the South, you're left trying to make economic excuses for the continuation of slavery, with the inevitable conclusion that, "oh, eventually they'd have stopped enslaving people because of technology," or some such.
And as for the Southern economy itself -- they made no bones about the fact that, to them, slavery and the economy were inextricably bound together.