Insurance is bought to cover catastrophic losses that one cannot afford. It is not gambling, and asking if it is worth it because you probably wont get your money back is to miss the point.
Take life insurance. Losing a breadwinner for a family is financially catastrophic. If they could afford the loss, then why was the breadwinner working in the first place, and not sailing his or her yaught? There is no way to set enough money aside to cover this loss (self insure) for most families until they are close to retirement. Fortunately the risk of death at a young age is small and the rate of death is predictable with a large group of people. The principal of insurance is that this group pools some money in the form of premiums, and the unfortunate family that has a loss collects from this pool. It is one of the modern marvels of actuarial science. Yes the insurance company makes a profit, but so does every other business that provides a useful service.
Actually, you could out-earn many insurance companies, as their liquidity needs force them to invest more money at highly liquid, low interest rates than even most prudent, risk-averse investors would.
That said, when I drove my brand new, fully-paid automobile off the lot a few months back, I didn’t “need” collision (it wasn’t mandated because I owned the car, not a bank). However, if I were driving it home and it got totaled, I wouldn’t have been able to replace it. When my mother-in-law’s cooking eventually burns down my house, I don’t have funds to replace it, and my annual insurance premiums that I’ve paid up until now would barely cover the down payment, had I no insurance and had invested the cash (not an option because the lienholder requires insurance). Lastly, I rarely use enough medical services to cover my insurance premiums annually. When my wife was hospitalized, however, her costs likely exceeded what we will ever pay in insurance premiums.
People, lottery and insurance are complete opposites. When you buy a lottery ticket youa entering into a riskier state, when you buy insurance you are entering into a less risky state.
Due to competitive pressure, premiums usually only cover settlements and part of administrative costs. Profit is produced by investing the premiums until they are needed to cover settlements. Usually in the bond market. Insurance industry profit pretty well tracks the bond market.