Amos, your observation is mostly correct and you're right that having lost a war is not a sufficient condition for a wealth of songs. There were quite a few German songs after loosing WWI and none I know of after losing WWII. Why not?
What makes the losers write songs is not just having lost alone but also the feeling that loosing was a deep injustice and the spirit of 'our sons will fight again and in the end our day will come'.
Except for the lunatic fringe (I don't know their songs and don't think I'm missing something here) there is no feeling in Germany that having lost the last war was a deep injustice and, completely different from the 1920s, there is no revanchism of any relevance.
In a nutshell,
after WWI: we have lost and we have been wronged and we sing about it (BTW, I write about feelings and not about reality)
after WWII: we have lost and we have to blame oursleves so why should we sing.