What’s frustrating is there’s an obvious and effective way to incentivise that too. You don’t even need to give up private prisons.
Just split the payment. The prison gets paid say 20% up front. The rest is paid out over the 10 years post release. If the inmate ends up back in prison, the rest of the payments are lost.
Basically, 80% of their income is made by keeping the inmates from reoffending. Kicking them to the kerb with no skills becomes a big loss. Job training, and a robust post release support network are suddenly money makers, rather than sinks.