Now you are getting into the finer points of extermination - bad extermination, good extermination, and common-sense extermination.
Any conversation about extermination must include a look at the intent of the people advocating it. Sherman - from his writings - was rather clear what he meant.
I don't have the quotes at my finder tips but if you deny Sherman advocated extermination of his enemies I may have to do a search.
Sherman was a WWII strategic bombing campaign on foot & horseback. If he’s a war criminal so is the WWII 8th Air Force.
The Sherman who lived in Louisiana before the war? He fought a hard war, a destructive war, but didn’t want to exterminate his enemies.
And you’ve opened up a massive can of worms concerning our conduct in WWII, Vietnam, and other wars. Do you want to get into that?