QR code needs alignment patterns (5 by 5 bullseye shape) at correct positions to compensate distortion, so that limits the actual saving from entirely omitting

QR code needs alignment patterns (5 by 5 bullseye shape) at correct positions to compensate distortion, so that limits the actual saving from entirely omitting the data because removing anything left of alignment patterns would not reduce the size. You also have to account for masking but that's a minor issue (the optimal masking algorithm is a recommendation and not a requirement).