The US doesn't have too many prisoners, it has far far far too many criminals, and the high incarceration rates are an inevitable product of that. The US needs to solve that problem first.
How many criminals are the offspring of other criminals? To what extent could the crime problem be solved in a single generation by ensuring that teenage offenders are locked up throughout their reproductively active years (instead of forever dipping in and out of prison on short sentences) to ensure that they don't reproduce?