I believe that every time you show your ID to someone, you compound the likelihood that you will suffer identity theft.
I encountered the issue when a doctor's office wanted to see my ID before they checked me in for an appointment. Further, they wanted to make a copy of my driver's license and save it with my electronic records. I asked how making a copy of my ID and saving it in a computer system that I do not control protected me from identity theft. I got an answer that had nothing to do with my question - they said that they wanted to make sure that my insurance wasn't being used fraudulently. I pointed out that they were protecting the insurance company, not me.
At that point, I refused, declining to show them anything but my insurance card. I stated that disseminating the contents of my ID puts me more at risk. I'd rather protect myself than protect the insurance company.
Getting frustrated with me, the doctor's receptionist asked how showing my ID put me at risk. I answered like this, "Show me your driver license for five seconds and I'll have your name and license number memorized. Give me a total of ten seconds with your card and I'll have your address, too. What kind of damage could I do with that information?" This disturbed her. I didn't even have to go into my mistrust of the integrity of their Microsoft computer systems with the wide open WiFi access to the HP Laser Printer behind her.
"Are you going to refuse me service?" I asked. She backed down and has never asked for my ID since.
I do not have eidetic memory, however, I've practiced memorization techniques to help my aging brain. If I were a professor, I would be categorized as an absented minded, forgetful one. I believe that almost anyone could easily learn the memorization trick.
The doctor's office could easily set up a "secret passphrase" system to verify my identity. Rather than ask for my ID, they could ask me to regurgitate a phrase or password that I set up at my first appointment. They get verification, I get to protect my private information.
Wait a minute, aren't I risking a lot by having that blurred image of my drivers' license at the top of this page? Couldn't somebody "unblur it"? Well, it's highly unlikely. Even if they could find some way of doing this, they'd find my name is "Karen L", I was born on March 45, 1910, the license expired in 1886, and my ID number is the same as my ZIP code. In other words, it's not an image of a real license.