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Grant also had to deal with Halleck in the Department of the Missouri, and there was a Department of Ohio, and a Department of the South (Gen. Sherman). The interplay (or failure of it) between Departmental Commanders and the commanders in the field is almost always discussed in the various Civil War histories.
The South also had departments (eg., the "Department of North Carolina") but it's not clear to me at the moment how they used them, and only had a few short periods where there was a "General of the Armies) (Lee twice, early and late; Bragg, late). Sometimes historians cite the South's lack of interest in inter-theatre cooperation as one reason they lost the war.
Finally, I note that Division leadership changed MUCH more often in history than it does in the game. Division commanders were often replaced because their superiors felt that they didn't follow orders fast enough, or didn't take advantage of a situation. Commanders also were replaced while wounded. These sorts of replacements happened on both sides.
For example during 1862, "Winder's Division" was commanded by him until KIA, then by Taliaferro (wounded, as I recall), then by Starke who is not even in the game. This all happened in a matter of months. Changes on the Union side were common as well.
In the game, we usually put the best commander (based on his very conveniently laid out stats!) we have in charge and leave him in charge until he's killed (rare) or a better commander comes along (more common). We don't replace commanders for failure to perform, since we know something the original commanders didn't: their stats. There is a potential fix for this, in which a commander loses his division if he fails to win a battle, or to force march, etc. Another leader would have to be appointed while the first guy goes back in the pool to await another assignment. This change would not be automatic, but there would be a chance for it, perhaps based on his stats or his political rating. Length of service in the position would ameliorate the chance to be replaced.
As for the "department" (theatre) commanders, and the General of the Army positions, it's less clear to me how to insert them.
Comments welcome.