Simplest solution - open up all states to all insurance companies, like auto insurance, and then require people to either buy insurance or post a bond allowing them to not have insurance. Every single insurance company would go into a price war with every other in trying to offer low rates to young healthy people.
Why does health “insurance” have to be all things to all people?
My auto insurance doesn’t double as an engine maintenance plan. My homeowner’s insurance doesn’t cover repainting dingy rooms.
Why can’t I buy insurance against disasters and pay the routine stuff from my own pocket?
They actually make their money via an explicit profit load (and also from investment income on their reserves). They build the average claim level into their rates, which means people who incur low claims (like you mention) offset those who incur high claims. The problem you alluded to is that if insurers are forced to cover anyone who wants insurance then people are more likely to wait until they are sick to buy insurance, which will raise the average claims cost and therefore raise premiums, making insurance less affordable.
Similarly, denying claims (where appropriate) keeps insurance more affordable. The biggest problem in health insurance is that the person “buying” health care services is for the most part not paying for it. Yes, they pay for the insurance, but when it comes time to “buy” health care services, they want the Cadillac regardless of cost because the insurance company is paying for it. No one thinks in the abstract that unnecessary utilization is going to raise premiums. This is where insurers can step in to control unnecessary utilization. Studies have shown that you can achieve lower utilization and higher quality. Most providers are paid on a fee-for-service basis, so the more services they provide, the more they make. So they have little incentive to control utilization, and in fact, the threat of medical malpractice claims encourages unnecessary utilization. This resulted in the insurer stepping in to “manage” the level of care as insurance became unaffordable. During the economic boom years, people rebelled against managed care restrictions, and as a result insurers backed off. But as premiums rose, pressure increased to find some new way to control cost. “Consumer driven healthcare” emerged, where the idea is that there is more member cost sharing so that the consumer (the patient) has more skin in the game, and therefore makes more prudent purchasing decisions.
I agree with your point that denying claims is not how they make their money. Claims are usually denied because they are for a service that is specifically excluded from the coverage the person purchased or because the service is not deemed to be medically necessary (which can be a judgment call, and the patient can appeal the decision). And besides, they build the average expected claims into their rates, which would reflect the degree to which claims are denied, so if they denied more claims, it would ultimately mean lower premiums, not necessarily higher profits.