"Most" insurance is not for Acts of God, but for small, discrete, predictable, and uncorrelated risks: Life, health, automobile, homeowners / renters, property & casualty (usually structural fires), theft, burglary, and business-related risks.

It is major and widespread disasters which private insurers typically avoid, specifically because many policies receive claims at the same time: flood, earthquake, hurricane, and increasingly of late, wildfire. An alternate term is force majeur, which might offer a clearer image of why such widespread events are uncovered.

<https://www.investopedia.com/terms/a/act-god.asp>

Other common exclusions are for civil unrest and acts of war.

I'll note that the Investopedia article above includes tornadoes amongst its events. This somewhat suprises me as tornadoes, whilst locally devastating, often do limit damage to a highly localised area or path. Yes, large storms or clusters may devastate a city or region, but most events are reasonably small-scale, as major natural disasters go. A widespread hailstorm could well be far more costly in terms of claims, as discussed in TFA.

Insurance works by predicting the future value (or cost) of a particular event, and by spreading that cost out over a large number of policyholders. On the back-end, insurance companies operate through reinsurers, who bundle those already-bundled risks into even larger tranches, and hence, more predictable outcomes. The ultimate private-sector backstops are entities such as the Lloyds Names, in which high-net-worth individuals pledge their entire personal assets against particular risks. (The nature of this and the potential downside cost has been much commented on over the years, and there have been periods in which there have been spectacular personal wipe-outs as a consequence.)

Where private companies can not or will not tread, governments frequently step in. Flood insurance in the US is frequently offered or backstopped by the US Federal Government. This is one of numerous ways in which governmment enters into and manipulates risk markets, with other examples being Federal Deposit Insurance (on bank and savings and loan deposits, see recently Silicon Valley Bank), exemptions from liability as with the nuclear industry, and backstopping other financial instruments as with Fanny Mae and Freddy Mac in the home mortgage sector.

And there are instances in which insurance companies have stepped away from their obligations. My understanding that this was the case in the 1906 San Francisco Earthquake and Fire, argued in part by insurers on the fact that records of both individual policyholders and of the insurance companies themselves were destroyed in the event. I don't know what the antecedents of US state-based regulation of insurance are, though I suspect that this event played a role.

One view of government is that it operates where the private sector can not or will not, generally, notably in national defence, in various risk and safety-net systems (notably the modern social welfare state, in many ways born under Bismark in Germany in the late 19th century), as an establisher of standards (from money to measurement to industrial specifications), and as a provider or coordinator in the case of public goods: those whose marginal cost approaches nil, which are nonrivalrous in consumption, and/or which are non-excludable in consumption.

This gives rise to the observation that the US Government is an insurance company with an army:

<https://archive.nytimes.com/krugman.blogs.nytimes.com/2011/0...>