This type of billing practice causes a mess of winners and losers, essentially unless your insurer has good pricing with wherever you end up getting treatment (often not a choice you get to make in an emergency), you can end up holding the bag for the cash price, usually half of the $10k number you mention. Quite ridiculous when other insurers are paying less than half that price, smells of a scam.
What’s ironic (?) is that by mismanaging a scheme to get everyone on private insurance they’re really working towards socialized insurance. Which good or bad, there is no going away from once you have it.