The problem with your Rand-esque proposal that if we all saved and lived below our means would be rolling in it, is that we don't all have the privilege of living in state or region that provides reasonable healthcare.
Any guesses what a family policy with a $10,000 (?!) deductible goes for in Maine? $1,400. Say what? That's if you don't get insurance through your employer, which is becoming more rare everyday as insurance negotiations for employers gets stupid expensive everyday too. That's approaching 30% of my annual salary, and we'd have to pay up to $10,000 before anything kicks in.
Oh, and routine medical visits aren't covered either, so that just encourages you to not see a doctor unless you really need to. Who honestly wants to drop $200 annually to have someone with 5 years of med school tell you you're fine, but could lose a little weight.
The system is broken. If you're covered by insurance you have no right to speak to any of this. If you live in a state where individual policy pools are cost effective, you have no right to speak to any of this.
The state of the matter is that the rest of the world has figured this out. And while there will always be challenges figuring out when $84,000 for open heart surgery on a 90 year old man is warranted, we can do better than right now.
TLDR; Health care that's twice as expensive and general health that's not even in the top 25 in the world anymore. And no, people go to Thailand for really expensive experimental surgeries (done by American doctors, granted), these days.