Do you actually believe that if the CSA had become independent then everyone would have lived happily ever after? No, it would've been constant war for centuries. It would've been like the fucking Balkans. Even if the Union had conceded defeat for the time being, they definitely would've waited to build up strength, and then gone right for another try at unifying the country again.
Besides, the CSA never would've survived on their own. They had no major industry besides agriculture... and slaves. Go figure.
Other countries would let this happen?
Generally, a super-power doesn't take kindly to someone invading one of its trading partners.
Once the Confederacy gained independence, they'd have been taken under the wing of the European powers, simply because they'd provide cheap(er) supplies. If any wars were to be fought from then on, many of them would support the Confederates with more than just materiel shipments.
And to be clear, I support the Confederacy, because of my beliefs regarding a people's right to self determination, regardless of what reasons they have for it. Were they free from evils during this era? No. But nor was the Union. One simply has to look to what they view as the lesser of two evils.
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