The issue with healthcare is that providers have leverage over insurers, not that there is a lack of competition for insurance.
How is a discerning buyer supposed to choose insurance based on anything but price when that is the only information available?
Then there's the entire bureaucracy that is medical billing. You have to know which obscure codes for diagnosis can be used with which, similarly obscure, codes for treatment. None of those codes ever exactly match what is happening to the patient, so you have to choose one that is close enough and hope the insurance agrees.
You ever wonder why it takes 6+ months to get a medical bill? That's why. It has to be processed by the medical billing bureaucracy until it bears only the slightest resemblance to reality and then shuttled back and forth between the provider, the insurance filing system, and the insurance underwriter. Only once that is done can they send you a bill.
How much cheaper could providers offer service if they didn't have to pay dedicated staff to play some perverse game of telephone with the insurance company?
Capitalism just means private people control the capital, rather than the state. Beyond that and you’re in different forms of capitalism. There’s no requirement of competition.
Even if that is true, in some areas companies' interests strongly misalign with that of citizens. An insurance company earns more by rejecting customer declarations. An ISP earns more by giving customers less bandwidth for a higher price. A toll road company earns more by doing as little maintenance they can get away with, while keeping prices high.
Yes, in a perfect market, customers will flock to competitors that are better for them. However, in many cases a perfect market is not attainable for various reasons. E.g. because the cost of entry is too high (e.g. making a competing ISP would require you to put your own fiber in the ground) or because there are network effects that are nearly impossible to break.
This is why certain markets need strong regulation or government monopolies -- to protect people from pure profit seeking. Health care is a good example. Health care in Western Europe is much better, while less money is spent on health care. This is because health care is strongly regulated and insurance companies cannot f*ck over customers. The objective function of maximizing profits becomes a constrained optimization problem, which generally leads to other ways to increase profits, like pressuring pharmaceutical companies to lower prices of medicines.