In this song "über allen" :-) "über alles" has some negative overtone, unfortunately
Discussion
While I don't agree with much of the authoritarian negative overtones (undertones?) that you allude to... I disagree with the fear of them even more. Germany should restore all three verses, but probably shouldn't invade Poland... at least not too much of it anyway.
It's very true what you wrote about authoritarian/totalitarian regimes, including not just nazi/fascist but also the communist/socialist. Unfortunately I don't know the verses so I can't comment on that.