In the Confederacy, all it took to keep out of the meat grinder was to own 20 slaves.
I can think of a couple of valid reasons why this makes a sort of sense.
Firstly, 20 or more slaves could be a problem if the person who is responsible for them is not around to keep a problem from starting. The Southerners were deathly afraid of a slave revolt, and so I can see where they would be greatly concerned about a large number of slaves in one place without supervision.
Secondly, presumably someone with 20 or more slaves is providing services for the war effort, and in terms of support, they may have been regarded as more valuable where they were, than any service they could render as infantry.
I am reminded of the movie "The General" in which they refused to enlist a train engineer because his expertise in keeping his engine running was regarded as more valuable to the war effort than would be his service as a rifleman.
So strictly from an practical perspective, this deferral makes a lot more sense than some rich guy paying $300.00 to get out of the fighting.