Despite the high incarceration rate, the US is ranked third in the OECD for homicide, fourth in rape, eighth in robbery, sixteenth in assault, thirteenth in burglary and tenth in vehicle theft in the OECD. The US generally also jails people longer than most other countries; the ratio of people in prison to people who get convicted per year is much higher than in other countries, and those weren't the first "tough-on-crime" laws by any means.
And so for the highest imprisonment rate in the world, amongst the OECD the United States is still amongst the top half of the 32 OECD countries for every category of violent crime. It's not like these are short-term effects either, we've been jailing people under three-strikes for a generation going on two. It's pretty clear evidence that a high rate of imprisonment is not actually reducing crime.
https://www.civitas.org.uk/content/files/crime_stats_oecdjan...
There are certainly other factors, like the presence of a large group of “othered” people with less opportunity, but there is no doubt a vengeance streak running through the American conversation on criminal punishment.
> According to official ballot materials promoting the original Three Strikes law, the sentencing scheme was intended to “keep murderers, rapists, and child molesters behind bars, where they belong.” However, today, more than half of inmates sentenced under the law are serving sentences for nonviolent crimes.
https://law.stanford.edu/three-strikes-project/three-strikes...