I kinda agree with your OP. Everyone should be required to have health insurance, but only for high cost medical expenses. That would be a catastrophic care policy that pays for expenses over a certain amount--maybe something like $4-5K per year for each adult, and $500 yearly per child. The best way to do this is through single payer, non-profit insurance. And it must be mandatory for 2 reasons:
1) When as much of the population as possible pay premiums into the system, it spreads the risk over the largest number of people. Thus, the premium becomes as low as possible for everyone.
2) If you allow people to go without insurance, the cost of their care is shifted onto those who are insured. If they wind up in the ER with an injury, or some other health crisis (as they may be eventually) they must be treated until they're stable. That's a federal law (
EMTALA.) But their costs are ultimately added to what all the rest of us pay. Which increases everyone else's health insurance premium. The uninsured are freeloading on all of us who do buy insurance. And don't say that EMTALA could be repealed, because that's not gonna happen.
Then, the insurance companies can sell optional supplemental plans to customers who want their deductibles covered. It shouldn't be that expensive because the carriers' liability--at most--is limited to the deductible amount. This framework is based on the Medicare model, which is simple to understand, and is well-accepted.