That viewpoint ignores risk. You pay a small premium to shift a risk onto a different party. Whether it's a net benefit to you depends on both the premium and your valuation of the risk. Self-insuring is often not efficient.
It makes more sense if you think about a group of people. If there is a 1% chance of getting into a car accident that could cost $1 million in medical bills, it is economically inefficient to have 100 people keep $1 million each in liquid funds for such a contingency. Insurance creates value by allowing those funds to be allocated to more efficient purposes. Out of that value, the insurance company takes a cut to compensate it for its risk, and each individual gets some economic benefit for having shifted that risk to the insurance company.
Not saying that's the case here, but in general insurance creates value by eliminating inefficient contingency funds.
That makes sense for insurance where the "upside" (for lack of a better word) is very high - say, millions. Very few people could save millions in liquid assets, and for most of those who could, a million dollar event is still catastrophic enough that it makes sense to insure against.
But, as in this case, when the upside is capped at a fairly low number, which is entirely achievable in savings for most people who could afford the premium in the first place, savings are by a wide margin preferable.
It makes more sense if you think about a group of people. If there is a 1% chance of getting into a car accident that could cost $1 million in medical bills, it is economically inefficient to have 100 people keep $1 million each in liquid funds for such a contingency. Insurance creates value by allowing those funds to be allocated to more efficient purposes. Out of that value, the insurance company takes a cut to compensate it for its risk, and each individual gets some economic benefit for having shifted that risk to the insurance company.
Not saying that's the case here, but in general insurance creates value by eliminating inefficient contingency funds.