“They did so, of course, despite the official CSA policy banning them from doing so, ...”
Yes, that was “official” CSA policy, but remember that the Confederacy was just that, not a monolithic union of seceeding states. For example, some Tennessee units actively recruited and armed black soldiers and integrated them into combat units as early as 1861. Many people in the South volunteered to serve their state first, and only secondarily the “cause” of the Confederacy.
Quite agree. And there were various Home Guard, militia and state troop units throughout the war, most of them viewed by CSA soldiers as havens for draft-dodgers more than anything else.
My point is that banning blacks from serving as soldiers was explicit CSA policy, and any blacks that served did so in violation of this policy.
The Union itself, while more centralized in administration than the Confederacy, was not the monolithic system we have developed since. If most of the northern states had refused to support the Lincoln administration, there is little he could have done to coerce them, particularly during the early part of the war.