"Acts of War" are generally excluded from insurance claims, but not civil unrest AFAIK.
I think the idea behind that is that in an 'act of war' it is generally a nation-state acting against the entire US, and there are likely to be many claims that could quickly bankrupt an insurance company. Furthermore, unlike fire or flood, there's really very little that any insured can do to mitigate damages from acts of war.
I don't know how many insurance claims were filed following the Sept 11th attacks but I'll bet it was in the tens or hundreds of thousands. Were they paid? I honestly don't know.
I do know that the US Government had (and AFAIK still has) an office where people who were harmed by the 9/11 attacks can submit claims and the US government pays them, but I don't know if, for example, they have to wait until they get a denial from their primary insurance before applying, or whether filing a US government claim precludes them from filing a claim with their insurance company.
I also don't know if the INSURANCE COMPANIES have the ability to file a claim for what amounts to indemnification in the event that they have to pay claims related to 9/11. It would be an interesting question but not germane to this topic, I think.