The latter part of 64 and the rest of 65 saw the Confederate front line forces shrink very quickly, down to about 120,000 men whereas it is very possible that they should have fielded five to seven times that. The complaints of the conscription officers were not so much about desertion (which was very high) but of the laws of the states and the Confederate laws that kept thousands of Confederate military assigned behind the lines. In fact the major complaint was that while front line units were always short of their assigned complement of men, those non-combat units or front-line units were always overmanned to the point of duplication or triplication of required functions. Official shirkism was a plague upon the Confederate Army.
Emory Upton's observation that the conscripts, by law, could not be taken out of their own states, as a major cause to the Confederate defeat is something to think about. I'm not playing favorites (or maybe I am because of the name-- LOL) but General Upton was a really smart man and had a great post war career in American military science.