No one wants health insurance.
No one wants a drill. What they want is a hole. The way to get the hole is to buy a drill.
Same thing with health insurance. Owning health insurance does not guarantee your health any more than owning life insurance does not guarantee you will not die.
You buy health insurance for one reason, and only one reason. To cover the financial bills that accompany a major illness or accident.
Insurance is based on the premise of indemnification which means "to make whole". If your car is stolen, your insurance will indemnify you (subject to policy limits) and put you back in a car of similar value. You don't get your original car, nor do you get a brand new car, even if your car is only a few months old. You get the value of the car that was stolen.
Same thing with health insurance.
You may or may not get your health restored to 100%, but that is not a function of the insurance. What you will get is at least a portion of your medical bills paid by the carrier so you can move on with your life.
You can certainly buy sore throat insurance that allows you to see the doctor any time you have a sore throat and only pay $10 plus another $10 for the medication. And you can buy ingrown toenail insurance, and acne insurance, and dandruff insurance but these kinds of plan will be very expensive.
You have to wonder if it is really insurance when you are trying to cover things that can either be anticipated and planned for, or can be covered from a savings account in the event you suddenly come down with an ingrown nail.
When you have that heart attack, or you are run over by a truck, you really don't care about the piece of paper that says Big Safe Company Health Insurance Policy. The policy does nothing to ease your mind or pay your bills. You can't take your policy to the hospital or doc and expect them to thank you for showing them your policy. They really don't care who the carrier is. They just want their money.
Similarly, while it is nice to be able to see a doc for $10 you should be more concerned about how you are going to pay $150,000 for a liver transplant. If you get a sore throat and don't have $100 or so to see the doctor, chances are your throat will get better in a day or so.
If you need a new liver, you really can't put that off and there are not many doctors (and hospitals) willing to sell you a used liver on the monthly installment plan. The health insurance plan collateralizes your liver transplant, making it possible for you to live a long and healthier life.