Yes, yes, yes, and other methods. These are called "Electronic Shelf Labels", and there's a whole slew of competitors.
WiFi is very high power, so its "pull only twice a day" kinda setup. You have a radio that only turns on twice a day to contact the server. Zigbee is also a solution, though that requires a Zigbee router (coordinator? I forget the terminology). Much less power on Zigbee, but if you're deploying hundreds/thousands of these ESLs, I think the benefits of Zigbee low power outweigh the penalties.
NFC exists but I don't think I've ever seen them in person. Probably too much effort since it'd require a human walking around the store?
I've even seen ESLs that work off of infrared. You're supposed to install IR LEDs all around the store, and they can it all shelf-labels to update. IR receivers are the lowest power, so this is the only way you can feasibly "push" data to a shelf label. (Wifi and Zigbee are "pull only").
So some computer blasts the IR signal around the whole store, which is enough information to transmit to change all the prices apparently. Like a giant broadcast remote control.
Sure, you can't do it today, but I'd be surprised if we don't see it in 20 years.
I don't know if they have batteries and wi-fi, or if they're updated manually with NFC, but either way they can't be too expensive if there are 5000+ in every store. They're a bit smaller than the badges these guys made, but they might be a lot cheaper and easier to work with.