Chief Justice of the US Supreme Court Harlan Stone called the Nuremberg Trials a "sanctimonous fraud" and a "high grade lynching". Justice William O Douglas called the series of trials spanning 1945 to 1949 as an illustration of "power over principle". Hangman M/Sgt John Woods told Time magazine "10 men in 106 minutes, that's fast work". Strangely enough it's hard to find the total of Nuremberg executions. The popular figure seems to be around 500 and maybe close to 1,000 while it's easy to find that the Japanese artosities resulted in 93 executions of war criminals. Was justice really served? Did the popular media demand blood or were the Allies showing their political clout to Russia while ignoring Japanese criminals?
Actually, the number of criminals executed as a result of the far east trials was probably also about 1000. The difference was that each country tried the criminals it had in custody.
But let's get real here. The war had cost 70 million lives, many of them civilians and a lot of them executed in violation of their human rights.
The world wanted justice. They wanted someone to pay for all that misery.
Also, the world had learned it's lesson from the last war. At the end of WWI, the Kaisers of Germany and Austria were allowed to abdicate, and live in exile. None of the ministers or generals who instigated the war were held to account for it. (Save, maybe the Russian leaders, who were executed by their own people.) There was no disincentive for the next generation of politicians and military leaders to start a new war.