I think there's a sort of weird subtext in the "risk pooling" discussions on this thread that "risk pooling" is a way for people who don't replace their old roofs to get protection from the people who do. But that's not at all the concept! You refusing you repair your roof isn't an act of god; it's just recklessness.
1. pre-emptively dropping or refusing coverage
2. claim inspectors concluding the company has no liability for a particular incident.
It doesn't all need to be #2 (and probably should not be), but it also doesn't all need to be #1 either.
Also, it depends on the jurisdiction, but while the insurer can try to void the whole contract, courts don’t always let them do it, especially if the policyholder convinces the court it was an innocent mistake or oversight rather than a deliberate lie.
(When I bought a house, the sales contract was maybe 50 pages. I went to the escrow company to sign. The escrow agent was visibly annoyed that I leaned back in the chair and set about reading every page. One of the pages that needed to be signed said nothing but "I have read and understood this contract.")
Except, Courts have ruled that you can, at least sometimes, get out of the fine print of a contract by claiming you didn't read it. For example, see the notable 1962 Supreme Court of California case, Steven v. Fidelity Casualty Co [0].
In 1957, plaintiff purchased a life insurance policy covering plane crashes, from a vending machine in Los Angeles, with his wife as the beneficiary. His itinerary took him from LA to Chicago, and from there to Dayton, Ohio. On his return from Dayton to Chicago, he'd scheduled a one night stopover in Terre Haute, Indiana. In the morning, he went to the airport in Terre Haute, and was distressed to discover the flight had been cancelled due to technical issues, and he was going to miss his connection in Chicago. The airline agent referred him to a charter airline, who organised a charter flight for him and a handful of other passengers back to Chicago. Sadly, the charter flight crashed, and he died.
His widow sought to claim on the life insurance policy. The insurer denied the claim, on the grounds that the fine print of the policy said that it only applied to scheduled air carriers, not charter flights, and hence the flight on which the insured died was excluded. His widow sued the insurance company in the name of her deceased husband. The trial court sided with the insurer, on the grounds that this clause was clearly stated in the fine print of the policy, which the policyholder was expected to have read, and he had signed to say that he had.
However, on appeal, the Supreme Court of California overturned the judgement, and ruled for the widow. It held that, for consumer insurance contracts, any clause or exclusion which the policyholder could not have reasonably expected, must be pointed out prominently, not buried in the fine print. Since, it ruled, the policyholder had no particular reason to expect the exclusion of charter flights, and the insurer had not prominently stated that exclusion in the policy (e.g. by using a larger font), it was not legally binding.
And, from what I understand, the rule established in this 1962 case is followed in California law to this day, and has also been adopted by the courts of several other US states
I don't know if it really is the case that your insurance can be voided over material misrepresentations unrelated to your claim, but certainly there's no moral argument that it shouldn't work that way.
This doesn't stop expensive lawsuits, even if they ultimately don't pay the claim.
Whereas your ability to sue for a non-existent policy (or one where that was unambiguously canceled) is... much less.