Insurance has a societal benefit, in the sense that it spreads risk around the population as equitably as it can. I'm not required to have car insurance to drive in California because the nanny state wants to protect me from myself. I'm not required to have car insurance to drive in California because some insurance company donated a bunch of money to the relevant politicians. Both of those things might be true, but that's not why I have to have car insurance. I have to have car insurance to protect everyone else from me, and vice versa. The alternative is a world in which many more people have accidents and go bankrupt or sue each other for damages, and that's a worse world for everyone, even the people who never get in an accident. Insurance is like a low-pass filter for tragedies.
Health insurance is a similar situation. Access to preventative care, or just being able to see a doctor outside of an emergency room situation is a lot less expensive in the long run for everybody. Medicare and Medicaid costs (that all taxpayers eventually have to shoulder the burden of) scale with the health of the population on Medicare and Medicaid. Giving everyone the opportunity for health has a selfish reward as well as a humanitarian one, even if you don't care about poor people being able to see doctors when they have problems. It's much cheaper for everyone in the long run. This necessitates solutions in between the two extremes you presented.
It very well may be what's best for society, but it's definitely not insurance.
Do you ....know what insurance is? Optimization based on feature of the population is not part of the definition. If a million people all paid into a pool that would cover any one of them if they got sick, and they all paid the premium, that would still be insurance.
If you want to pay extra for faster or 'better' treatment maybe you can get insurance for that.
As a society, the cost cutting measure should be based around buying in bulk and forming deals where a given area has at least enough coverage capacity contracted (presumably via some dutch-auction like mechanism) to cover projected needs.
If the point of insurance is to flatten the price of health care to something everyone can afford, then the cost is the sum of all health care expenditures for a period, not the health and precrime health of Joe Mightgetrectalcancer.