Conservation is not just about preserving info, it's also about not adding information that's not here. If you upscale without those gradients (effectively sharpening to the max with nearest neighbor extrapolation) you introduce high frequencies that could not exist in the original data. You've created new information out of nowhere.

But of course you're correct that in this case it may be the desirable outcome. I still think that this idea of creating information using algorithms in order to get a subjectively more pleasant result is really one of the biggest issues of our time. Not a day passes where I don't see AI-colorized pictures, AI-extrapolated video footage, AI-cleaned family portraits, AI-improved smartphone footage etc...

It's both amazing and a bit scary, because in a certain way we rewrite history when we do this, and since the information is not present in the original it's very difficult to ascertain how close we truly are to reality. We're creating a parallel reality, one Instagram filter at a time. Maybe that's the true metaverse.