This leaves no room for "reasonable" edits, like resizing the image. Most sites you can upload images to use some form of image compression that would also kill this as well.
If the signature was kept through edits, then it's no longer actually linked to the image contents and is just added fluff for the appearance of trust. No real way to discern if an edit materially changes the content or not (the reasonable assumption is that most edits do change the content).
If the sig isn't kept through edits, then this would only work for directly shared images with no middle man hosting compressing things in the middle (at least if it wasn't 100% reversible compression).
This could be useful in a lot of situations and use cases (like press releases and news articles), but it simply wouldn't work for so many other image sharing situations.