The 'proper' fix is to either engineer cameras that can focus closer, or to engineer barcode scanning apps to be able to see a code which is small somewhere in the frame.

I think people are working on both as we speak.

It doesn't matter how objectively good your camera/decoder is, in absolute terms. There will always be some minimum size or maximum distance, where the detail can no longer be resolved (or errors no longer corrected)

If we're talking theory, the pixel size doesn't matter - it's the amount of information encoded in the QR code that matters (ie. excluding ECC bits!). In turn, that means it is theoretically possible to decode a QR code where each 'pixel' of the code is smaller than the pixel of the camera sensor observing the code.

While it is theoretically possible, nobody has yet done so...

Why? Is this something that's a side effect of some irrefutable physics law or a limitation of the current technology?

Both. You can't have a measurable feature smaller than the Planck length, but that's not relevant to QR decoding in any practical sense.

As for the practical limits, try using your phone to take a picture of something very far away, or very tiny, and see what happens.