I truly doubt that the vast majority of these people were war criminals. Yet that didn’t mean that there weren’t a lot of people that wanted to kill them.
For example, anyone who had been in the SS, not just the genocidal General SS, but also the combat Waffen SS, would be killed on the spot by either the Russians or the Americans, but the French were willing to draft them into the French Foreign Legion. So even entire Waffen SS battalions ended up wearing French uniforms and fighting in French Indochina, aka Vietnam.
Germany was also devastated at the end of the war, so many emigrated just to get out of there. And South America was a preferred location, as many Germans had migrated there around World War I, and there was a large and prosperous German community.
It should also be noted that many German POWs interred in the US during the war liked what they had seen, and wanted to emigrate to the US as well, and did.
But some, like Eichmann, were. And the Argies gave him a lot of help.
I had a retired U.S. Marine friend who did join up after his release here in the states. He was a German infantryman during WWII and saw action in Russia during Operation Barbarossa. His prior cold weather training saved many lives up near the Chosin Reservoir.