Here's an two year old OP-ed explaining why they are a bad idea:
The cold hard facts about America's private prison system
Snippet:
...With the government paying private prison operators about $23,000 per year per inmate (keep in mind, the minimum wage is $15,000 per year), it’s a lucrative business. CoreCivic’s reported 2017 revenue was close to $1.8 billion, and a back-of-the-envelope calculation shows that with 80,000 beds supported by the government to the tune of $23,000 per inmate per year, it’s collecting about $1.8 billion annually from the government. Business is booming indeed – thanks to the American taxpayers.
To boot, with most private prison contracts, if the prison beds aren’t full, the government has to pay for them anyway. For example, in 2011, Arizona paid Management and Training Corporation (MTC) $3 million when a 97 percent quota wasn’t met. (By the way, this payout came a year after three prisoners convicted of homicide escaped Kingman – an Arizona state prison run by MTC – after workers ignored alarms indicating a breach. The escaped prisoners murdered a retired Oklahoma couple before being apprehended...)
...The Sentencing Project found that from 1999-2010, CoreCivic spent on average $1.4 million per year on lobbying at the federal level, and employed over 70 lobbyists at the state level. In addition, the largest private prison companies are members of the American Legislative Exchange Council (ALEC) – a public policy organization that has developed model bills for state legislators to use when proposing “tough on crime” initiatives.
This means that private prison companies, which benefit from having more prisoners, inevitably influence legislation for longer sentences, like the 1994 “three-strikes law” which imposed a mandatory life sentence on anyone convicted of more than two serious crimes. Not surprisingly, between 1992 and 2003, the number of people serving life sentences increased by more than 80 percent...
...in 2018, private prison companies donated $1.6 million in federally disclosed contributions to the midterm elections.
This private prison cycle of lobbying, donating money to campaigns, and getting more prisoners with longer sentences in order to squeeze out as many taxpayer dollars as possible, is a perversion of our judicial system. And it doesn’t even take into account the cheap labor many of these American companies receive from prisoners for as little as 17 cents per hour.
The economics are on the side of keeping as many people as possible in prison, for as long as possible...
All things being equal... I'm not particularly sold on the idea private prisons are a good idea...