The miracle of US healthcare is how at every step, work is done to minimize every party's ability to either use market power to lower costs, or to make people cost-conscious about their own expenses.
Insurance, in a vacuum, detached from an industry is a perfectly sensible way to try to spread risk. And as you say, this fair, reasonable insurance isn't about getting extremely rich, but about being the best at identifying where the risks are, and using market power to lower costs. But with healthcare, and especially with the US peculiarities, we manage to get minimal value out of it.
People getting care don't know their options, and how different the pricing can be. Insurers are capped by a percentage of services paid, so they really are happy if everything is very expensive. Providers band together into conglomerates that make sure it's hard for insurers to lower reimbursement rates. Pharmacy benefit managers build complicated schemes that let them take a bigger piece of the pie. They even purchase pharmacies, and restrict the expensive purchases for themselves, while the local pharmacy is squeezed. All in all, it gets very expensive, with minimal control of spiraling prices, and nobody that can lower costs is incentivized to do so.
We blame insurers because that's the people that get paid first, but yes, it's not really a matter of just insurers. It's a kafkaesque system that is basically impervious to significant reform. And for good reason: Every dollar we overpay is someone else's salary. A decrease in costs per person for the same care to match, say, Spain would involve a whole lot of people making a lot less money, including many losing their jobs. Not exactly a political winner, even though the country would be better off with more efficiency