That's a great what if despite what we currently know of these prisons and what we know of private companies seeking profit at the expense of whatever you're stating.
There's a country in the 30's that used misinformation to sell what you're suggesting and they, at one point, had a thriving prison system in less than a decade.
Don't be so polyannish.
So if I follow your logic here you feel the same about grocery stores being private? Because if they were run by the U.S. government you wouldn't have 47.9 million people (about 1 in 7 Americans) living in food-insecure households? All because a private company that employs people are tryng to make money?
SRC: https://www.ers.usda.gov/topics/food-nutrition-assistance/fo...