Given that current jail conditions are dismal as best, I see no reason for private companies to not offer for-pay incarceration services that solve these problems. This is no different than private companies offering delivery services because USPS sucks, or private transportation companies existing because bus infra simply isn't good enough. If a judge considers these options prison-like enough, then I see no reason they cannot exist.
Does it suck because not everyone can afford it? Sure
Does that mean we should just screw everyone equally simply to claim we're fair? IMHO no. Not unless you also want to close down UPS, FedEx, and Greyhound. And not unless you are willing to come out and openly say that YOU consider rape, abuse, and neglect to be an official part of our rehabilitation strategy (because that is all that county and federal prisons excel at)