> use the massively diversified risk pool
Diversified risk doesn't reduce average costs, it only averages the cost across everybody. Doing this generally raises average costs significantly by making people insensitive to price, resulting in over-consumption, i.e. unnecessary tests and procedures. We already have this problem with employer-provided coverage, but covering more stuff makes it worse.
> plus minuscule administrative costs (compared to private insurance)
Most of the administrative cost of private insurance is related to investigating insurance fraud. Doctors and patients can still collude to claim procedures were done without actually doing them and then keep the money, so somebody still has to do that. Putting it in the police budget instead of the Medicare budget is an accounting difference. It doesn't actually save the money.
Also, the administrative costs of private insurance are only a small percentage of overall healthcare costs.
> price negotiation power
Passing a law that everybody has to pay taxes for an insurance program which then out-competes private insurance by having a taxpayer subsidy and becomes a monopsony is not "negotiating" prices. It's price controls. It allows Medicare to set whatever price they want because the provider's alternative is having no patients.
They can absolutely dictate lower prices that way, but then more providers go out of business. It's less profitable to make new drugs and new medical devices, so fewer companies do and we get fewer new drugs and new medical devices. Things that could have been cured then have to be treated. How much does that cost, in terms of both money and lives?
Also, how does it address the real causes of high healthcare costs, like the shortage of doctors (and medical residency slots), or the difficulty of getting generic medicines approved by the FDA without a patent holder to pay for the clinical trials, or the lack of price transparency that causes patients to choose providers without respect to cost differences?
> for the larger benefit of society?
How many programs claim to be "for the larger benefit of society" and then go on to be worse than the status quo?
Once upon a time it was easy to point to bread lines as an example of this not working. Today it's more subtle. First they regulate private industry in ways that produce inefficiency and reduce competition, then the effects of bad regulations are used as evidence that the market is broken and we need more regulations.