The reason for the CSA conscription was much more simple and less political, the harsh reality of life in the PACS made the draft a necessity. Nobody was volunteering after 1862. It wasn’t the fighting or the cause they hated, it was the the neglect, lack of proper clothing, the feast or famine and the 20 mile hell marches.
Not to mention a long line of veterans now in the local communities on 1 leg or missing an arm, or wounded is some other horrible manner. The effects were the same North or South, enlistments tapered off after the cold hard brutality of the war became apparent. But throughout the war, volunteers still made up the vast majority of the soldiers. Figures I saw some years back indicated that between 8-10% of the Union Army and maybe 10-12% of the Confederate army strengths came from drafted men.
So let's see if I can follow your logic here:
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