I don't see any reason why there necessarily would be. Generally speaking, compression algorithms do better when adjacent pixels have similar colors, which is t

I don't see any reason why there necessarily would be. Generally speaking, compression algorithms do better when adjacent pixels have similar colors, which is the unshuffled state. In cases where there is a version that compresses better, unshuffling might not work. If you had an "pinstripe" image consisting of alternating black and white columns of pixels, obviously it could compress better after being "shuffled" with all the similarly colored columns together. But then this algorithm would be unable to get the original image back.