"Medicare for all willing to pay 10% of taxable income" seems like a way to sneak universal healthcare through the political backdoor. It will initially have a funding shortfall due to adverse selection (it will attract primarily people with low incomes, high risks or both) but you would gradually move all public subsidies towards that program and remove all incentives, tax credits and rate protections from those who choose the free market option, and when just a minority still hangs on to the private providers, you make the 10% health tax mandatory to all.
The way I see it, you will never wrestle away the trillion dollar bone from the mouth of the US healthcare industry, but you can make it wither away indirectly by creating a better universal system and dismantling the status quo. It's not like Europeans are forbidden the option of private insurance, it's just that it can't take hold and grow to control a significant part of the spending because everyone can see it's not the solution that will save you when you will get really really sick.
The way I see it, you will never wrestle away the trillion dollar bone from the mouth of the US healthcare industry, but you can make it wither away indirectly by creating a better universal system and dismantling the status quo. It's not like Europeans are forbidden the option of private insurance, it's just that it can't take hold and grow to control a significant part of the spending because everyone can see it's not the solution that will save you when you will get really really sick.