The same argument could be made for incest which is mentioned in the Bible. Slavery simply could not have lasted.
I agree, but the question is for how long. I think your belief that it would have been no more than a decade is unrealistic. Having fought a war expressly for the defense of slavery and including clauses in their constitution expressly forbidding the outlawing of slavery, it seems highly unlikely that just a few years later they'd ban the peculiar institution.
While it's possible that some slaveowners would have individually seen the economic sense of emancipation and freed their slaves, I think slavery as a legal institution would have survived well into the 20th Century. Keep in mind that mechanization and advances in pesticides didn't reduce the need for intense labor on cotton until the 1940s.
It would have lasted a lot longer than the 10 years you mentioned because emancipation had three major strikes against it in the eyes of Southerners. One, there was nothing to replace it. Two, it was profitable. And three, if you end it what do you do with all those free blacks suddenly wanting rights and all?