No, that isn't exactly how insurance works, and it would be almost pointless for individuals if it did work that way.
Instead, it works by bucketing risk. In the simplest form, everyone is in one bucket, ignoring individual risk. That means that all other things being equal (e.g. size and value of your house), despite you have low risk of your house flooding, you would be paying exactly the same premium as the person who who has very high risk because their house is built on a flood plain.
Of course people paying more for their risk than it warrants may see that as unfair - so insurers use more buckets - e.g. bucketing high, medium and low risks.
But there's a delicate balance here - for instance, insurers may just decide not to insure the high-risk category. Or even if they do, the premiums may be unaffordable or the insurance benefits substantially restricted. And the natural extension of categorizing like this is to put an individual in a category by themselves - and then to limit payout. Essentially making the insurance not any better than a savings account, and probably worse if you don't claim at the beginning of the policy, before there's a large pot in the savings account.
From the point of view of perfect capitalists, the insurers would like to insure people with negligible risk, for high premiums, for low benefits - to make the most profit. From a social-good point of view, we would like insurers to cover risk that people cannot control (e.g. genetic risk) for reasonable premiums and good benefits. Categorizing lives somewhere between these two - a kind of necessary un/fairness.