I guess the idea is that you put a deductible amount of money into the account annually, and the tax-advantaged investment makes up for any difference between the deductible and the savings you get on premiums for having a HDHP (I.E. HDHP premiums + deductible - tax savings ≈ normal premiums + deductible).

It's an insane way to run health insurance, and it just goes to show that expected value and mathematical benefit isn't the end-all be-all, but it's supposedly mathematically coherent.

It's mathematically coherent, but it's value relies upon the assumption that we are already spending thousands out of pocket (but it's not taxed).

I prefer the option of don't spend thousands out of pocket, pay taxes on the unspent income. If I'm paying 100% of my healthcare costs, what good is the health insurance?

Here I think it boils down to whether one thinks it's okay for everybody to spend tens of thousands of dollars per year on medical care, as long as they (probably) aren't bankrupted.

If so, then they are probably more likely to view "don't bankrupt me bro" as the use case for health insurance, rather than "I need affordable medical care".