One answer (assuming that we’re comparing UHC to private health insurance) is that there are a number of reasons why private health insurance, as a concept, is fundamentally broken.
Here are two of them:
(1) For most businesses, one of the things the “invisible hand” of the free market does is give businesses an incentive to treat customers well. If you go to burger king and order a burger and get a rotten burger full of maggots, or something, the negative publicity burger king will get, the loss of repeat business from you and everyone else who sees the maggots, etc., will FAR outweight the savings that burger king might gain by relaxing their quality standards enough to let maggoty burgers slip through. That’s because every transaction burger king ever has with a customer is for a fairly small amount of money, so they would lose far more by generating customer badwill than they would by making a really cheap and terrible product (well, more than it’s already arguably cheap and terrible).
Health insurance is different, however. There are some number of individual customers who are going to develop diseases and conditions that require millions, if not tens of millions, of dollars to treat. So poor Joe comes in to the insurance company and says “whoops, I have developed a nasty condition that requires $100,000 of treatment every month for the rest of my life”. At this point the insurance company can try to find some means, legal or illegal, to avoid having to pay out. And if they do, they’ll presumably suffer some negatives of badwill and loss of patronage and negative publicity and stuff. But unlike in the burger king case, where they’re weighing negative publicity vs a $3 lunch transaction, here they’re weighing negative publicity vs a really huge amount of money. So the “invisible hand of the market” actually gives insurance companies a strong incentive to be ruthless and evil. (You might ask why this doesn’t apply to other forms of insurance, and to a certain extent it does, but the big answer is that health insurance has SUCH a hugely varying range of money that different sick people are going to need. With house or car insurance, there’s generally a fairly easily calculatable worst case (the house is entirely destroyed), so there aren’t these freak outlying cases which suddenly cost huge amounts.)
(2) There’s the serious problem of preexisting conditions. Healthcare insurance companies want to make money. Therefore they want to insure people who are a good bet. So suppose you have one of these conditions which means that you are guaranteed to need thousands of dollars of treatment per month on an ongoing basis. No insurance company will, if it’s purely up to them, sell you insurance. At least, not insurance that will cost less than what you’re guaranteed to be paying in the first place. Why would they? Which means that if all insurance comes from private companies, someone who is unlucky enough to develop an expensive ongoing condition will never be able to purchase insurance at all. So either they’re totally screwed because they can’t get insurance, or they have to have been lucky/smart/careful enough to have already purchased insurance back when they were healthy… but at this point they’re totally locked into this one insurance provider, and if they lose their job, or get poor for a while and miss a payment, or fail to dot an i or cross a t on some piece of paperwork which gives the insurance company an excuse to drop them (which of course it has an incentive to do), they’re SOL.
Again, you might ask why this is different from any other type of insurance? Because if someone is such a terrible driver that they can’t get auto insurance, well, they can survive without a car.