You remarked; "but I would tend to agree with Lincoln on his "horrible math" as you explain it.'
Lincoln was absolutely right about his assessment of the mathamatics. But do you treat your army that way? Do you say to your soldiers that you are nothing more to me than a number that is expendable cannon fodder so long as an enemy is killed in the process? If that were precieved to be the tactics employed by a commanding General disillustionment would be the results. Soldiers are willing to risk their lives in Warfare, but they also expect their Generals to NOT risk their lives foolishly or recklessly.
I believe that Grant was called by Congress to account for his alledged usage of U.S. Colored Troops in that manner. U.S. Colored Troops, nor their families in 1864, could not vote. So why should Congress have cared politically? It would have been more politically advantagious to use them is such a manner to empty the Confederate cartridge boxes before sending in the white troops who could along with their families vote for them.
It was because the use of soldiers, Black or White, in that manner was not concidered to be humain even back then. Even in a war where humanity was a little concideration. It was only concidered to be a just use of such manpower in Lincoln's mind, who was the Commander-in-Chief.
But we still hear the cry today, "Nuke 'em all, and let God sort them out." But in 1863 that "Nuke" was your Army, and killed it also.