My insurer(s) policy states I have to claim from the airline first and only if they refuse will they entertain a claim.

just as my insurer requires me, if I get injured in Europe, to make use of the EHIC card and will not reimburse me for any costs that would have been covered by the EHIC even if I don’t have one.

it also says that if I have to cancel a flight they expect me to have reclaimed whatever elements of the fare I can such as government taxes and airport fees from the airline first - or will assume I have done,

other policies may differ.