Most cut out the middle man. the insurance company and have the money go straight into the health care.
I've experienced both systems, and they don't necessarily cut out the middle man. Here in Germany there are multiple insurers, both public and private, and all children (even ones that were stupid enough to get sick) get cared for. You can't make the assumption that the uninsured simply can't afford to have health care, the assumption is that the nation can't afford to let people go uninsured. Then the math changes.