That's why I liked catastrophic health care plans. Insurance works best when it covers rare, expensive events. Otherwise, it interferes with the process. My car insurance doesn't cover oil changes or new tires, but if I get I crash and injure someone, it kicks in. Homeowners insurance doesn't cover a routine roof replacement, but it will if there's storm damage. That's how health insurance should work.
A catastrophic health care plan has low premiums and high deductibles. You also get access to a tax advantaged savings account to save up for future events. So you can take the money you saved on premiums and pay for medical expenses tax free. Or let the money accumulate to cover future medical expenses or even retirement!