The problem with many existing health-insurance plans is that they cover the cost of routine treatment for illnesses, such as colds and flu that occur frequently, or the cost of care for conditions, such as pregnancy, that are heavily dependent upon the choices of the person who is insured. Basic economics teaches that paying for routine treatment via a third-party insurance company will raise the total cost of that treatment. This happens for two reasons: First, the insurance company, as middleman between the consumer and the healthcare provider, has costs that must come out of what the consumer pays. Second, insurance that pays for routine care lowers the cost of each doctor visit to the consumer, thus increasing demand. Higher demand with a given supply means higher prices.
As Miller alludes to, the problem with all third-party payer schemes is that they artificially increase demand for services, putting continual upward pressure on fees and, hence, health care costs.