We're talking about a single purchaser using its power to impose prices on suppliers. It's hardly unique - how do you think Walmart keeps its prices as low as possible? By leveraging their power.
And all your aguments seem a bit moot when you look at countries with single-payer systems - they just work, at a per-person cost that is far lower than the US
Walmart is subject to competitive pressure. If they squeeze suppliers too hard and quality suffers or some suppliers refuse to meet their demands, consumers can go buy products from a different retailer.
In cases where you actually do have a private monopolist, is is terrible.
> And all your aguments seem a bit moot when you look at countries with single-payer systems - they just work, at a per-person cost that is far lower than the US
In the US the medical providers have significant political influence which results in a regulatory environment that favors high prices and there is no reason to expect a single payer system in the same environment to change that.
In some systems the providers have less political influence, but many of those systems have long queues or refuse care on the basis of cost or have other deficiencies with no recourse.
It's also entirely possible to have a socialized system which is more efficient than the status quo in the US but less efficient than a system that actually exposed providers to competitive pressure. The cost efficiency of the existing US healthcare system is a bar level with the ground.
If they set the price too low, you get shortages or long queues or sacrifice quality and no one can do better because that would require charging more which isn't allowed.
If they set the price too high they're overpaying, which is what happens in any system where the providers have political influence, as is manifestly the case in the US. Then new competitors can't lower the price because it's set by corrupt politicians and more efficient providers can't return the difference to patients who choose them.