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A thriving private market is created> medical providers operate cartels that jack prices up.
These two statements are in direct conflict. If it were a thriving private-sector market, then providers wouldn't be able to form cartels that jack prices up.
I'd say Medicare is a good chunk of what's giving us the worst of both worlds. It's full of mandates that warp the entire system, but then fails to take responsibility for the warped system. Like sure we both agree that Medicare should fund drastically more residency slots. But my point is that the problem is Medicare doesn't actually have to pay the full cost of the high prices it has created with things like the residency slot shortage.
> where people's medical costs drastically increase, publicly-funded single-payer kicks in; before that, people with (actuarially) far lower costs
This analysis is entirely backwards on so many fronts. I'm not even really a proponent of single payer, but your point pushes me in that direction. Higher variance but lower average costs earlier in life are exactly where it would be most effective to spend public funds - keeping more people from financial ruin per dollar spent, more productive and enjoyable years of life, younger people are more likely to proactively obtain/consent to medical care, better outcomes from interventions being done earlier.
Imagine the opposite of what you're championing - use public funds to try to keep everyone alive until they've had 65 years of life, after which point part of your retirement savings would be a plan that determines how many resources might be spent on giving you a few extra years of not-so-great life. That seems both more efficient and more fair to me.