Inside of Schengen you don't need ID to fly unless your airline requires it (many LCCs do to prevent ticket reselling). I've flown SAS without ever showing ID -

Inside of Schengen you don't need ID to fly unless your airline requires it (many LCCs do to prevent ticket reselling). I've flown SAS without ever showing ID - just scanning my eTicket barcode at security and the gate. (You are required to carry ID when visiting another Schengen country, but it is not checked by airports like for extra-Schengen flights)