I’ve not heard of a corps of that small size, though I suppose outside of the Army of the Potomac they may well have existed.
But you’re quite right. In World War II The U.S. Army opted for the policy you describe for the South, through its replacement policy.
I just think that the idea of fighting a regiment as a skirmish line due to combat casualties is odd. But evidently that is how they did it.
Seems to me if you have all of these odd sized units around it would get confusing to command and make good decisions.....When you got brigades the size of regiments something is wrong....
The union fielded 8 corps of various sizes at Gettysburg. The South 3 traditional corps of roughly 30,000 each.