What is wrong with an Identity Card ?
In Continental Europe, everybody has one and must carry it at all time. People are used to it and nobody complains.
I'm not British, don't you hold passport along with you in your flightbag?
I don't see then what's the difference in term of privacy especially the one containing data chips with all your informations.
I've ID card, credit card sized, with limited visible info about me "not showing my private adress either" containing a chip of datas...and nobody was looking for it so far through digital readers.