QR codes generally want a marker on all four corners, so streaming one infinitely would mean that some of them would never be printed. You also need a certain amount of whitespace around a QR code so you can't just smush them together to make it looks like one infinite code. You might be able to make an infinite barcode though

Interesting connections with motion jpeg, animated gif and RFB (Remote Frame Buffer as used by VNC). The latter has me particularly curious, though all of them seem like mad hacks in search of faint excuses. Imagining a bi-directional link, still though, without any idea of WHY beyond "Because it was there".