I don't think that argument holds much water.
The Southern economy would continue just fine if they simply changed the status of slaves to paid laborers. Prevailing wages for farm hands at the time were very low, so it is doubtful such a move would drive the planters into ruin. Certainly, this would have involved a big transfer of wealth from the planter class to everyone else, including the majority of white Southerners who weren't planters. Forcing planters them to pay their slaves prevailing wages would have increased wages to all landless people.
The planter class still obviously had an interest in maintaining slavery in order to avoid this transfer of wealth, but that does not explain why secession received such widespread support from the non-slaveholding white population (which was a majority).
It was aspirational identification.
Even though the great majority of southern whites had essentially no prospect of rising to the wealth and status of the planter families, they were the ideal to which the rest of the workers in the economy aspired.
That’s why the spread of slavery was such an incendiary one after the Mexican-American War: working whites couldn’t hope to displace the entrenched planter families—they owned the good land in the existing slave states—the aspirations of the lower classes required the spread of slavery for the model to be sustained.
Freeholding northern whites, in turn, understood that this expansionist imperative was a direct threat to their aspirations, and they formed (with railroad financial support) the core supporters of the nascent Republican Party.