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The type of insurance would have differed according to the policy purchased. In a lot of cases, businesses would not have been fully covered. The specifics are usually private between each business and the insurer (often a contractual requirement of the insurer to reduce price table exposure to competitors). What coverage did exist has been disputed by insurance companies.
The insurance loss, while large, was not larger than commonly occurring natural disasters. For 9/11 the direct loss for insurers was approximately $32 billion. Hurricane Katrina was $71 billion. Natural disasters alone cost insurers $20 billion each year.
For more details on 9/11's impact on insurance specifically: Ten Years After 9 11 Property Insurance Lessons Learned.PDF