My impressions seems to be it's the combination of the 2
(1) people in the US will balk at paying others' healthcare if you ask them directly, so it "has to" be subsidized in a roundabout, inefficient way. ER is obliged to treat you regardless of money (and people do go there with routine concerns from my limited experience), but someone has to pay, so other patients get charged extra. That is really annoying in a way, and it's pure politics - nobody can come out and say "hey, you are paying for the poor anyway, so why don't we at least cut out all the middlemen - private and public, and just pay them openly"?.
(2) But the main one I think is that public option is basically impossible as long as you allow a viable private option, because everyone will take private option if they can and public option will get the worst-off, health-wise and financially, and as it gets worse as a result more people will bail, etc. You can look at schools as an example - private school parents literally pay double price, public system is easy to abuse via de-facto neighborhood class-based segregation, and private schools STILL thrive because private option is just THAT MUCH BETTER (in the consumers' opinion, at least).
If you really consider the implications of the 2, you can understand also how regulation drives up cost in another way than its actual overhead and supply-limiting effects - it regulates options out of existence. If I could go to a "private semi-ER" where they (1) get a good doctor, pay him double, but are let's say (2) not obliged to treat before payment and do not take Medicare, or maybe any insurance, (3) aim for 20-80 principle as far as equipment is concerned (i.e. somewhere in between ER and Urgent Cares), it would be the obvious, better, and cheaper choice. I'm pretty sure an "uber for Urgent Care" based on this would make bank AND benefit tons of people. Of course, it's regulated out of existence. Or consider a startup that would offer "Indian/Russian/Turkish/..." quality facilities, with an obvious price trade-off - it's impossible, because if it were possible the existing public-private frankenstein would simply die. You can see the same with schools, with activists constantly trying to stifle school choice, because with viable school choice public schools will simply die.
As a result, the system is both terribly inefficient and creates the worst incentives. Take me as an example. If I decide to retire early, I'd be helped greatly by ACA, and would optimize paper income and (ab)use it to the max. I do feel like it's justified because I am paying for it now in taxes; but I didn't do the math, so mostly it's just bad incentives + it was the govt who screwed up healthcare in the first place. So hey, ACA is good for me. If they had universal healthcare I'd stop working even earlier. But is that good for society?
To be clear, I support a fully free market option for both healthcare and schools, and the only redistribution allowed should be cash, and catastrophic insurance limiting total spend.