In fact, you’ll recall that a world war was triggered because a country wanted to exterminate a specific ethnic / religious group not only within their borders but also in their neighbors’ country.

WWII was triggered by Nazi Germany’s attempt to take over the world. Ending the Holocaust was just a fortunate side-effect of beating back the Germans and removing the Nazis from power. Nobody in power have a shit about Jews until people started seeing images from the death camps after they were liberated.