A sudden claim against many should be priced into the cost of the insurance, offset by some risk adjustment. The goal is ultimately price stability, if the price is not too high (that’s the unknown)
It’s the difference between getting cancer (calculable, but perhaps not high probability), and getting hit by a meteorite (not actually calculable, very severe consequence).
Or in many of these scenarios, can’t pay out, because they’re bankrupt. The biggest issue with black swan events (in the proper usage) is everyone is screwed because no one saw it coming and/or it’s so widespread no one can do anything about it for individuals.