The Year Zero plan makes no sense.
First off, what I like is that this particular plot draws inspiration from the real-world Chinese Cultural Revolution. You'd expect a surviving Nazi authoritarian regime would resort to this particular form of a "managed revolution" by manipulating youth rebelliousness.
What I find to be less believable is that the Himmler's regime wants to obliterate US history. Now, I don't think that a Nazi propaganda machinery, as effective as it was and as it would have become in the alternative 1960s would ever do a stupid thing like that.
This is a world where the Nazis and the Japanese, the two competing powers, each control roughly a half of what used to be the US, with a lot of American men occupying responsible positions, even the most high ranking ones, like Smith does.
And Smith, for example, and many other collaborators (in either policing or military capacity) had once served in the US army before the US lost the war. And who did they fight? Smith fought the Japanese, for example, and many others probably fought against Germans as well.
So, a Nazi propaganda machinery would probably use this anti-Japanese experience of the US history and blow it up. I don't think they would want to erase it. Similarly, the Japanese propaganda would probably like to stress that Americans fought the Germans twice during the 20th century in their part of the occupied US.
Therefore I believe that either Axis power would play up some parts of the US history, rather than obliterate it altogether.