Diversification? An insurance policy is a wager made with one party on a series of closely related events. There's nothing diverse about it, from the consumer standpoint. Some diversification is possible for the insurance firm itself, although there are limits to that so most firms purchase reinsurance.

Of course it's diversification. Instead of being short your own illness only, you enter a swap where you receive coverage for your own illness (thus being flat on that clump risk), and pay a small floating leg covering (a small proportion of) everyone's illness. You have much smaller variance, but the same expected return (minus administration costs) - just like any diversification.