Just about everywhere I went in Japan and China on my recent trip used qr codes - for every thing, not just menus.
Restaurants in Japan use either a qr code, or you order from an ipad.I can't remember when I last used a physical menu in Japan, although I used to prefer them.
I like eating dinner in an 'izakaya', which is a pub-style establishment where you order lots of small dishes. A qr code allows you to keep track of what you've ordered. To pay the bill you simply scan the code and walk out.
One of my favourite places to eat is Kura Sushi. I'm not a fan of sushi and don't eat raw fish, but Kura sells all kinds of small dishes. You never interact with staff members. (They are lurking in the background in case you have a question.)
Once you get used to it, it all makes sense.