There is no privacy to lose.
To be able to compare the facial image with the id, the system needs to already have a copy of the id image. It doesn't matter whether the airport scanner saves it recorded image or not, the authorities already have a copy of your face. They will also have all the info the require to track your journey through the airline ticketing system and banks used to processes the transaction used when purchasing the ticket. All the tech does is reduce staffing costs, and arguably improve accuracy, as the robots won't have a hangovers at the start of the day.