Launch insurance can absolutely be given to classified payloads. My understanding of the launch insurance business is you say "my payload is worth $(X)XXX milli

Launch insurance can absolutely be given to classified payloads. My understanding of the launch insurance business is you say "my payload is worth $(X)XXX million to me and we're launching on this type of rocket" and the insurers look at the history of that rocket and your history as a payload manufacturer and charge you a 10-40% premium that gets built into the cost to the government.