I’m sure you have been reading what the Japanese and Germans have been doing to our troops, civilians, hostages and especially Jews. Don’t you think the US did this to emphasize the difference between us and them?
I don't know what the motivation was. There wasn't much "political correctness" at the time. But I certainly don't think honoring the deceased German Nazi (or Japanese, for that matter) military personnel was appropriate at all. They were, after all, an enemy fighting to destroy the US as Americans knew it.
There should have been some established rules for the American military to deal with such situations, and they shouldn't have gone anywhere near this far in their respect for the enemy deceased. After all, if these Germans (or Japanese) had been captured alive, they would be, at the least, in prison for the duration of the war.
From reading about WWII and chatting with my late father, a WWII veteran, I can sense that just about all the top military brass in the US armed services would probably have become enraged if something like this had happened under their command.