Consider the example of food, in general. Demand for food is wildly inelastic - without it provided regularly, for your entire life, you _will_ die. If elasticity were the only consideration in pricing, we should expect food to be break-the-bank expensive, but it clearly isn't. What else is different between the healthcare and food markets?
(To be clear, I'm not defending the current state of our healthcare system. It's broken in a lot of ways, and is way more expensive than it needs to be. I'm just arguing against the idea that the cause of its dysfunction is inelasticity of demand.)
[1] https://www.forbes.com/sites/zackfriedman/2019/01/11/live-pa...
Because welfare (and subsidy) programs exist so people aren't desperate for food, just like people who are covered under medicaid are not desperate to pay for health services.
There is really no mystery here.
The government needs to regulate markets like this.