First, a few clarifications. Genuine insurance is a pooling against the risk of a non-intentional, adverse outcomes. Risk itself means that there is a known frequency distribution of the adverse outcomes. Given these conditions, it’s possible to provide a pool of funding large enough to cover the expense of the entire class of adverse outcome, if each person who chooses activity subject to such risk is willing to pay a fee such that, when added up, the fees constitute a large enough pool of funding.
Take a look at Peter Klein’s book, chapter 6:
Genuine insurance is not possible if persons who obtain insurance can intentionally act to trigger a payout. This moral hazard is the main problem with “insurance” schemes backed by government coercion. By stimulating demand for such government-backed “insurance,” the price of the good increases and resources are mis-allocated. So-called “health insurance,” then, is a vast government-forced subsidy program that results in an enormous waste of resources.
Now, there are two aspects to whether or not genuine insurance involves a similar process of increasing demand for and therefore, prices of goods being insured. One is that, even if it did have these effects, they would not involve mis-allocation of resources. The other is that the existence of these effects depend on whether or not the existence of insurance changes people’s behavior towards the insured activity. I don’t think there is a general principle involved here. If the existence of insurance stimulates demand for the activity, then prices for the goods will likely rise and resources will shift toward the activity. But, if it does not stimulate demand for the activity, then prices will not rise and resources will not shift.
As an example of the first case, suppose there is no hurricane insurance is offered to people who live along the Atlantic coast of Florida and, then, a company offers genuine insurance (accurately assessing what will happen and the requisite premiums). It may be that more people build on the Florida coast. Of course, even in this scenario housing prices may not rise, but the resources devoted to building houses on the Florida coast will increase.
As an example of the second case, suppose there is no insurance for accidental breakage of cell phone screens and, then, a company offers genuine insurance. It may be that no additional demand for new screens occurs at all since everyone who breaks a screen has it repaired or buys a new phone.
Take a look at Hans Hoppe on risk and insurance: