That's not a free market economy.
"it doesn't seem like America has anywhere near enough regulations to be considered true capitalism."
You can't regulate your way into capitalism because capitalism by definition means markets free from government interference. The more it interferes the less capitalism you have.
United Healthcare is a great example. The governments enforce these companies being a monopoly be restricting which companies can operate in which states, having an enormous amount of red tape and regulation, documentation laws, etc.
If it was truly "capitalism" the government wouldn't' get involved at all. Part of the reason that doctors are so expensive to see is because there is a board that the US Government certifies to allow them to control which hospitals are allowed to be teaching hospitals for doctors.
If it was true capitalism there would be no regulation there and any college could graduate doctors. This artificially keeps the supply lower than it would be. These are facts.