Demand is inelastic? Meh, my brother is living in Brazil and has been using a ton of private healthcare services because it's cheaper. Again, you're engaging in all or nothing thinking. As the price of LASIK goes down, more and more people use it. Americans go to the doctor less because it's more expensive. Healthcare demand is the furthest thing from an 'inelastic'.

Healthcare is bigger than just things that you absolutely need. Obviously, there are those things, but that's what INSURANCE is for. Then, when you are healthy, you can shop around and when insurance is too expensive and has too many items you don't need, you can instead get a barebones plan which would cover the things that you seem to be worried most about.

If a person failed to get insurance, well... that's not good. We shouldn't encourage that as a society. If someone runs out of resources and has to demand it from others, they are a burden and that is bad. If too many people do that, society collapses.

Obviously, there are going to be those people and I'm not saying we shouldn't care for them, but the more we have a socialized system--one that has a shared resource pool everyone takes from--the less efficient it will be because the incentives applying to individual encourage them to use as many resources as possible because they aren't the ones who bear the cost.