Homeowners insurance has broadened considerably from simple catastrophic fire coverage. Most claims are relatively small, and can involve things like pet bites, stolen property, guests being injured, wind damage, etc.
Simple Fire (HO-0) or slightly broader coverage (HO-1) essentially don't exist anymore for individual homeowners. HO-2 (Where the company says "We insure you for the following (long list) of things).") is also somewhat unusual now. People don't buy them unless they are very price sensitive. The most common type sold is HO-3, where the the carrier says "We insure basically everything, with the following exclusions (like earthquake and flood)."
(Actual policies are much more complex, but that's the basic idea.)
And in fact, you do get the best of both worlds, because any carrier allows you to choose a high deductible, like $5,000 or more. So you can self insure the small stuff, (which the carrier doesn't want to deal with anyway, because of the overhead of settling a loss) and feel comfortable if say a pipe breaks during the winter while you are on vacation and causes $20k of damage, you are not going to have to come up with that money somehow.
As has been said, that is home and some health insurances are for. Most people will never live in a house that is destroyed that prompts a home insurance payout, and if you are someone who has their home destroyed, you will get back way more than you would put in in a lifetime because the average likelihood of it happening is so low. But not having the insurance would wipe out your wealth - you lose the house and writeoff the loss and have nothing left after the fact, and at best you spend an entire rainy day fund with a mortgage on the land to rebuild, and even then you are doing significantly more impactful damage than any rainy day fund could account for.
Same with catastrophic health insurance. Most people do not get debilitating diseases that don't kill you but will require lifelong care like Parkinson's or Dementia, but if you do get one of them you would be destroyed trying to pay the constant upkeep costs.
And strangely? enough, both are often best handled by the state. In some countries property owners are not insured privately but by the township to avoid problems where disasters wipe out multiple homes and some people do not have such a rainy day fund to afford to rebuild. And first world countries provide single payer healthcare to make up for the rare catastrophic conditions. If you want to have these costs borne out across the entire population to offset the individual costs when they happen to you, having them be society wide is often the least expensive option.