Why did the Allies allow Germany to continue to exist after provoking two world wars?
Germany did not provoke the first world war. The Great war was started by Austria-Hungary and Germany went into the war as an ally. After that war, there was a humiliating treaty of Versailles that served as fuel for the second world war. They allowed the Nation to exist because they needed a strong ally and buffer against the USSR since they feared communist expansion into Europe.
Could they have ended Germany forever at Nuremberg?
They could have. Forever is a tough word though. If Germany was split into smaller nations or if they build a new nation from it they would probably face more Nazis, more guerilla warfare and so on. They wanted to exterminate the ideology and not the people in Germany since the latter would give nothing in return and ruin many things in the future.
The United States became an imperialist nation at the end of the 19th century because Americans wanted to expand overseas with their belief in manifest destiny.
