Just as a counter to the Nationwide experience, the annual insurance provided with Coutts/Natwest/RBS bank accounts has just changed to Allianz and they say specifically that they will cover the: “value of frequent flyer points, air miles or loyalty card points lost by insured person as a result of cancelling the services paid for with those points, air miles which is not recoverable from any other source”. I can’t remember who it was with previously but having looked into it in the past they also covered loss of e.g. Avios.
I guess this might be better in the UK forum to reach a wider readership.