“Much of what happened was done by undisciplined soldiers on their own.”
I believe Sherman wrote freely about the need to exterminate enemies; first in the South, later in the West (native Americans).
He is credited with developing “modern war.”
Did Sherman exterminate anyone? His idea was to destroy the resources (to the extent that he could) that the other side used to carry on the war. That’s not what WWII’s exterminationist regimes were doing — they went much further. It is what the US has been doing in so many of its wars.