Except that there are billions in agricultural subsidies and they are (at least intended) to manage the cost of food on store shelves. The government will pay farmers to
not grow food to control the supply. The government isn't fully running the show but it's absurd to assert that the government is incapable of everything and that only private business can get the job done!
Especially when you're being entirely disingenuous about your argument. I don't honestly understand how you can truly believe that corporate interests care more about people than the government. Perhaps you also believe that corporations are people, and at that point I guess I'd have to concede. If corporations are people, then they do care about people. It's just the one they care about is themselves.
Not every business is a cartoon mustache twirling villain but it's baffling to me to see the lengths people will go to to both outright dismiss the governments ability to do literally anything, and also that private enterprise can do it better.
Also the major sources of inequalities today go far beyond education, policing, and the justice system. Many of them are inexplicably tied to private enterprise. You don't want the government in charge of growing or distributing food. Well that's great. What's also great is that the cheapest food you can buy is also some of the most unhealthy trash you can put in your body. Soda is cheaper than water.