I guess the main purpose of insurance products, whatever the kind of insurance is - life insurance or insurance from accidents - is to keep us calm. See, from the perspective of economic rationality, insurance if not always but very frequently is not beneficial, and sooner brings in losses not gains. To demonstrate this, there is an instance. Imagine yourself being asked whether 2% is the big probality. I am more than just sure that the respond will be definitive in most cases - no. The answer is apparently right as, indeed, 2% chance is really minute, and at times is being just ignored when we deal with some choices even without awareness that we do so. But imagine that some potential threat might occur to your wealth. The chance is again 2%, and your again asked about the same question. Will the answer differ? Of course, the result will depend on the extent of severity of the potential losses. The numbers of the losses of 10 dollars and 10000 dollars you will treat way more differently. But still ,regardless what the sum of the loss is, you will take the probability with much more serious mood than if it was only hypothetically. Hence the loss-aversion will impose the feel to protect your wealth. And what is the best way to prevent the bad outcome with 100% as if not to buy insurance? So, I am leading to that, we pay in such cases, in the first place, to separate ourselves from thr apprehensive premonitions, independently whether the desicion is rational or not.
Of course, in here, I am not disputing importance of necessary insurance like social national ones, or at works where employers are forced to do so, because conditions of the jobs might be harmful to heath of the employees. I am talking about private insurance, which are so strongly represented in adds and basically live on money earned out of the wrong decisions of their clients.