Fundamentally, insurance is a type of contract in which one party - the insurer - agrees to indemnify and reimburse another party - the insured -- for loss that occurs under the terms of that contract. In the medical field, it is a business transaction between the insurer and the insured negotiating access to health care. Remember: insurance is NOT health care; insurance is a third-party means by which an individual may access health care, but it is not the only way to do so.
What is the purpose of health insurance? In effect, it is a type of bet - a hedge - usually against a catastrophic loss. The gamble, here, is one's prolonged state of health; and the insurance company, which largely creates the market and sells the products, can be aptly described as a casino -- and like all casinos, the odds are in the house's favor.
For the average individual, the bet is "will your health undergo some catastrophe in some unspecified future?" It is unlikely that the average person will but life is unpredictable at times, and emergencies are not all that uncommon. However, if one were to occur the individual could ultimately lose their life for lack of financial means to pay for treatment. If the average individual is insured then the likelihood of death, or even just lack of treatment, is minimized because insurance pays out for those medical services. Purchasing insurance, by paying the "premiums" for that specific insurance contract, therefore, protects one against the risk of total catastrophe by guaranteeing a payer for needed medical/health services.
However, as with all bets, there is (at least) one other side -- namely the house, i.e. the insurance company. Though the process is nuanced, the unavoidable fact is that insurance companies bet against those whom they insure. While the individual wants access to health care in moments of crisis, the insurance company wants to not have to pay for that emergency health care at all. Even the goals of the two parties do not align: the individual wants to be as healthy as possible, the insurance company wants to make as much money as possible. Similarly, the ultimate goal of a healthy public is at odds with the goal of the insurance companies.
In these contemporary times, health insurance has come to mean more than catastrophic coverage; it now includes check-ups, minor surgeries, diagnostic imaging -- in short, ALL health care, not just catastrophic coverage. What has not changed is the ultimate goal of insurance companies: profit -- or more precisely, as much profit as possible. There are multiple ways to do this, but primarily they do this by getting a lot of paying customers (in order to pool that money, which creates a type of health fund for members) and denying coverage, ultimately payment, for any number of reasons that they dictate -- remember: they make the rules and, like employers, they have the power advantage in this legal dynamic.
So... a couple things to keep in mind: first, there is already a bureaucracy between the patient and doctor, and that bureaucrat is the insurance company. The company also gets the final say when it comes to insurance specifics (since they write the contracts, which are all but impossible to negotiate); they determine contract pricing with patients, doctors, and hospitals; they require authorization for services, procedures, and medications deemed medically necessary by physicians; and ultimately shape health outcomes in significant and structural ways.
Second, the insurance company is neither a friend nor an advocate for people, patients, doctors, health care, and least of all: public-health outcomes. Like all private businesses they seek to make profit, and as much of it as possible -- an "ethos" informed by the logic of corrupted self-interest. And again, they make money by selling a service that they want their consumers rarely to use in order to minimize costs and maximize profits. And there is no shortage of evidence of insurance companies doing just this; for example, the "pre-existing condition," used to be a legitimate and legal justification for insurance companies to either deny insurance coverage entirely or certain treatments for patients with such conditions. This is no longer legal due to the Affordable Care Act (ACA, a/k/a "Obamacare") and so now insurance companies must cover these people and pay for treatments related to those pre-existing conditions.
Third... well, there's more than three but this heads-up should suffice for now. Just remember: health insurance is not health care, it is a contract for access to health care; and, those who sell those contracts -- because they're primarily motivated by profit -- have goals that are necessarily antagonistic to the goals of those who buy those contracts.