Are you seriously arguing that people are wrong thinking while misusing the term "costs" in capital letters three times?
Consumers don't pay "COSTS". Consumers pay "PRICES." This is a fundamental concept in economics and lacking comprehension of it means no discussion of economics is worthwhile. If consumers didn't pay prices that included profit, then the entire system wouldn't function.
The insurance company negotiates "PRICES" with the hospital/hospital network, set where the hospital can make a profit (even if its non-profit, since they can then use it to expand, increase pay, etc). Or the uninsured individual pays a considerably higher "PRICE" for the same treatment both because of the laws of economy of scale, because hospitals can write off losses at higher rates for non-payers in those cases for tax benefit and because collecting from self-pay accounts requires additional man hours and almost always results with a higher Accounts Receivable average.
Individuals and employers pay insurance PRICES, set by the insurance companies for various plans. Those prices do include profits. They have to pay for advertising, lobbying, claim processing, price negotiation and maintenance of price lists, bill collection from employers/purchasers of insurance, legal fees, executive pay and yes profit for shareholders as well as paying for healthcare itself.
This is why Medicare/Medicaid has much lower costs. First, they set prices, rather than truly negotiating them. A single procedure will cost two different amounts at different hospitals even with the same insurance, but not under government coverage. Second, they don't advertise, they don't negotiate, they don't have shareholders or profit, they don't have bill collection. Medicare overhead is 1-2%. Private insurance varies from 11% to 30% depending on what you include.