The system would neither be free, nor will it be as expensive as private health insurance costs now as the cost is diffused within everyone living in the U.S.. Everyone that lives in the U.S. and works will need to contribute some portion of their income. It is like military expenditure, I seriously do not care as much as someone in another state getting hit. Likewise, I'm quite sure someone in another state could careless if my city got hit. But the cost to upkeep individual military operations would cost a lot more if border protection were completely state driven than it would be if every state contributed to the military that protected every state.
But like I said, it would be a transaction of parts of the medicare system and social security system into the new system that has a broader range which mitigates the cost a lot more than the two system currently have.
Also, do you know what the idea of a pooling system is? It would be something like contributing to a lottery group. Everyone that wants to be part of the group needs to pay a certain amount of their money. If, by any chance, one of the ticket hits the jackpot, everyone who invested in the group will receive a portion of the jackpot.
Theoretically speaking, you spend less to be part of the lottery group that gets 5 tickets each week than it would of cost you to buy 5 tickets yourself.