Okay, so in the end I went to my favorite bar in the evening because the place was jam-packed the whole afternoon and my buddy was busy. When he finally found time, he took the job very seriously: we shot a pretty convincing series of simulated COVID certificate checking using various methods.
Best of all: because it was nighttime and the light at the front door was pretty dim, reading the QR code turned out to be really, really difficult, further highlighting how much better a solution NFC is. Okay I’m being a bit disingenuous if I’m honest: many people will present an image of their QR code on their phone. Still, it shows NFC is a convenient alternative, and there’s always gonna be people who will come with an unreadable piece of paper anyway.
Check it out (faces and names blurred to protect the guilty 
):