Why do you assume that? Murder rates in the US were 10 times higher than in continental Europe even at the beginning of the 20th century, long before support programs existed on either side of the pond. (Indeed, in Europe, all the modern support systems, government welfare, and gun control hasn’t reduced crime—at least homicide rates—at all. Homicide rates in England, France, and Sweden hit modern levels in the 1920s: https://ourworldindata.org/uploads/2013/03/homicide-rates-in.... Germany and Italy saw major drops in the early 20th century, but I’d probably chalk that up to increased political stability.)
In the same units as that graph, WWII would likely register as over 1000 in Germany (compare with the less than 2 indicated in the graph).
White Americans are substantially more likely to be incarcerated than Western Europeans, but not as substantially as the non-race differentiated number might suggest. White Americans are incarcerated at a rate similar to Russia.
I can't speak to the drug war in Europe, or if it exists, but it is a likely culprit for a large number of American incarcerations. 1.3 million arrests a year are for "possession only"[2] and the number of Americans in prison takes off late 80's early 90's as the drug war is ramping up [3].
My understanding of the American incarceration system, and this is mostly just my synthesized view from reading and thinking about it, I can't easily source this anywhere - is that there was a lot of crime in the late 80's and early 90's, especially in major cities. People realized that basically all violent crime is committed by relatively young men. So - they devised a system where a significant number of problematic young men (1 in 9 men [3]) are locked away for a period of time.
1 - https://en.wikipedia.org/wiki/Incarceration_in_the_United_St... (Under "Ethnicity" heading)
2 - http://www.drugpolicy.org/issues/drug-war-statistics
3 - https://www.sentencingproject.org/criminal-justice-facts/