Sort of a tangent, but I wonder if there are any EU countries that have mandatory biometric ID cards. After a cursory (5-10 minute) search I found countries that either used to have ID cards but currently don't, used to have biometric ID cards but currently don't require biometrics, or have biometric ID cards that are optional. It does seem likely that in the future some country will, if it hasn't already, concede and mandate ID cards that contain biometrics.
Practically, anyway, GDPR seems like a much more effective measure.