There's a lot of instances where the government did a good job as well, and almost every instance where the government gave up something to a private company to run it the costs went up. For example the private prison system is garbage that has severe implications besides just costing much more than when it was all government run. When student loans were no longer government ran everything went down hill and cost us billions not counting the students who owe{d) immense money. Perhaps the best way to do it is to have what you suggested, medicaid competing against the insurance companies, but as is the system needs to be more than just insurance companies or you are screwed
I don't know anything about private prison systems. It doesn't make much sense for the government to convict someone and then turn them over to civilians to incarcerate them. Free market business operates on customer service, customer satisfaction, quality control, and profit... hard to find a reason for a private prison to operate on satisfying the customers, so I get what you mean.
Student loans are something different. Education costs money, and if they want the education, someone has to pay for it. If they apply for the loans, they agree to the terms, they sign the documents, and they spend the money... they are bound by contract to pay it back. They know this going in. I have no sympathy for them... I have children myself that are still paying back their student loans.
Regarding healthcare... you seem to blame insurance companies for everything, and you believe that creating anything that will undercut and destroy them will make healthcare cheaper. It will not.
Take "Medicare for all" for instance. Medicare is for seniors, and doctors accept Medicare because it's only for the seniors. They will make less, and it will take them much longer to get paid, but they do it for the seniors. Most of what they make, and what keeps their offices running, comes from employer based medical insurance. Now suddenly, Medicare is available to all... employer based insurance cannot compete, and is destroyed. Do you believe they will just accept this? No they won't. They will no longer accept Medicare, and they will only accept private insurance, credit, or cash. People become doctors because they want to be rich, it's not about taking care of the sick... at all. If they can help people, that is what justifies their income.