So you admit that having big money involved in the prison system is the source of corruption.
By having small individual contractors provide for a non-profit government entity you minimize the amount of money controlled by one hand. Their power and payoff from bribing a judge/DA is minimal. At worst, they may get fatter contracts and some prison officials get kickbacks.
By having large for-profit prison corporations with a direct financial incentive per inmate, you absolutely maximize the risk of false imprisonment. By concentrating the profit, a tiny piece is enough to easily buy judges for even greater direct profits. You have fewer people controlling more cash with less oversight.
Sorry, but I reject your “capitalism is bad” malarkey. You have given NO EVIDENCE of any sort or source to prove your prejudiced speculation. Come back when you have FACTS and not speculation.