It's a thought but I suspect it's incorrect. The harshness of prison policies peaked in the 1980s to 1990s. Private prisons really started booming in the late 1990s and the 2000s. But the trend since then in policy has been a softening (somewhat) of retributive policies. California's involvement with private prisons for example is largely in this decade, in response to court orders requiring reduction in overcrowding. But it past the country's harshest three strikes laws (where people were getting life sentences for a third non-violent felony) in the 1990s. But it softened that a bit a couple of years ago.

I think the most you can say is that private prisons (and public prison guard unions, which is probably a much bigger force) are slowing the retreat from 1980s/1990s retributive policies.