Exactly. Most health insurance plans are really pre paid health care, and not really insurance. If the patient paid for his own routine care, but had insurance for catastrophic events, then costs would drop.
What Medicare does is provide hospitalization free, and pays 80% of the rest for a monthly fee of around $150, depending on the age of the recipient. A supplemental plan is required if you can't pay that 20% of the $500,000 bill accrued by having cancer.
Here's the Dittohead Not! plan: Gradually drop the age for Medicare, not all at once, but a little at a time. Meanwhile, change the 80% flat payment to a floating rate from 0 to 100%, the 100% kicking in after the patient has paid 10% of his/her annual income for health care. The patient could, of course, purchase insurance to cover that 10%, or could have a health savings plan, or simply take his chances. Choices. Eventually, Medicare would start at birth. We'd have a real Medicare for all system that would cost far less than what we have now.