I can imagine a homogeneous population resulting in a lower crime rate although I have no data to back that up. I think a low crime rate makes it possible to have higher quality programs like this.
Assuming equivalent distribution, the higher the amount of people, the higher the amount of extremely difficult cases.
Let's skim those very difficult cases off for the moment: why can't the US make better use of concepts like restorative justice and rehabilitation for the rest of the criminal justice population?
It's cheaper; it's more effective to reduce crime; it's better for the children involved; etc etc etc.
So divide the jurisdictions to where they're manageable. We already do this - each state runs their system independently, just as each EU member state does instead of having a single European prison system.
This argument of scale comes up time and time again in these type of discussions despite being totally invalid in most cases: In most instances that are up for discussion it is not necessary to build one single large system.