Steel man counter-argument: health care is weird and different and special in lots of ways.
The people who need it most are often the least profitable to treat and the least able to pay for it. That's because being sick negatively impacts your earning potential. The sicker you are the less you can afford a way to pay for treatment to not be sick. It's analogous to the problem with debtors' prison.
Obscure or low-survival-rate conditions are almost by definition unprofitable to treat. Rare condition? Stage four cancer? It's most profitable to let you suffer or die. There's not enough of a market for the former and the latter has a low probability of leaving someone behind to pay the bill.
Old age care can't be profitably offered on insurance or credit. Old? Pay cash or die.
Demand is not infinite because (excluding certain neuroses) people generally do not want health care. They only get it when they need it. Demand does not skyrocket with reduced price or free availability, so the system doesn't automatically just drown in demand when you take the cost away.
Competition is sparse because talent is scarce and the cost means there tend to be only one or a few hospitals covering an area. Specialty services and general practitioners are different, but for advanced and expensive care it tends to be not quite a natural monopoly but almost one. It's like how there's not very many space launch companies. Because it's so f'ing hard the supply of competitors is small.
Lastly, because customers are ignorant (very few people are qualified to evaluate health care tech or treatments), quackery is structurally more profitable than medicine that works. It's hard to have a healthy market when fraud is massively easier and more profitable and the customer finds it hard to tell the difference. Add to that the fact that try before you buy and comparison shopping are almost impossible, especially for serious medical care. You can't exactly toss out or return a surgery.