It would be interesting to see corruption prosecution rates of judges sending people to private vs public prisons. All i can really think of are the 2 kids for cash judges, i'm sure there are plenty of unpaid corrupt judges as well.
In some states, the issue is not the private prison lobby, it is the prison guard lobby, which can be quite strong, as they may have a near monopoly on the provision of such services.[1][2]
And most of the laws people on here don't like (I'll add cerfew for teenagers to the running list) were instituted long before we had a non-negligible amount of for-profit prisoners.