I feel like this situation is overstated a lot. Something like 8% of prisoners in the US are in privately run prisons, which could be a problem, but it's not the massive number that is often implied.
As far as lobbying, the other 92% of prisoners are guarded by very powerful public sector unions, whose incentives are the same.
The existence of even a single for-profit prison provides a perverse incentive to put the marginal criminal into a private, profit-generating cage rather than a public, tax-draining, politically-risky rehabilitation or diversion program.
Furthermore, it is an invitation to corruption. Remember the judge that was sending juvenile defendants to a reform camp, often regardless of the merits of their cases, because he was getting kickbacks from the camp?
For the other 92%, how much work does that state-run prison contract out to private companies?
Quick, off the top of your head: do you have any idea just how many people are incarcerated in this country, in both absolute and per-capita terms, and how those figures compare to, say, every other country on Earth?
8% of the US prison population is a HELL of a lot of people.
That still means there are millionaires out there lobbying to keep drug laws as is so they can keep filling their prisons. And the other 92% of prisons probably have a ton of people behind bars due to drug laws because of the 8% of prisons that lobby for & profit from them.
Jobs, graft, construction, maintenance, slave labor, etc. - huge sums of profit derived from the government prison system, far more than in the corporate system.
As though the 92% of that equation is looking to give up its jobs and tax dollars. Because we just know how much the government likes to give up its spending.