To say the Sherman and Sheridan went "looting and burning" is to apply an unprofessional eye to their mission. Their acts were not random or wanton, or uncontrolled; and their purpose was not to enrich the Union, the Leaders, or the soldiers.

They were on a specified mission to designed and executed to crush the spirit of the South and to destroy their ability to resource their army and themselves. It was to ensure that the Populace of the South understood on no uncertain terms that they had been defeated when the army surrendured and the capital capitulated. Otherwise they would have likely slid into a long drawn out insurgency with the possiblity of follow-on warfare.

Which leads to the other great strategic lesson from the ACW that was ignored by the Friench and British, even though Wilson was there to remind them: The importance of being gracious in victory in order to secure the peace that your military has worked so hard to produce.

I believe strongly that Hitler is far less to blame for WWII than the French and British delegations at Versaille were.

So:

The importance of the will of the populace in wars between nations (vice Kingdoms); and
The importance of being gracious in victory in order to secure the peace.

Two great strategic lessons from the Amerian Civil War. Grant led the way on both counts; and his President understood and backed his play.