We have vaguely similar, but smaller versions, of the system you are talking about in the US. They are called "self insured entities" and are typically companie

We have vaguely similar, but smaller versions, of the system you are talking about in the US. They are called "self insured entities" and are typically companies that bankroll their employees directly. They typically hire a professional insurance company as a "Third Party Administrator" to handle administering claims. I am unsure as to their efficacy, although scale certainly affects their performance.