The problem with that is the content is usually shot with the certain definition in mind. If you don't film certain scenes from scratch, they can end up looking weird in higher definition, simply because certain tricks rely on low definition/poor quality, or because you get a mismatch between old VFX and new resolution, for example.
It's a widespread issue with the emulation of old games that have been made for really low resolution/different ratio screens and slow hardware, especially early 3D/2D combinations like Final Fantasy, and those that relied on janky analog video outputs to draw their effects.
For a specific simple example: multiple Star Trek TV series were shot with the assumption that SDTV resolution would hide all the rough edges of props and fake displays. Watch them in (non-remastered) HD and suddenly it's very obvious how much of the set is painted plywood and cardboard.
One somewhat funny example of this is in the first ST:TNG episode "Encounter at Farpoint". In one shot, the captain asks Data a question, and the camera turns to him to show him standing from his seat at the conn and answering. At the bottom of the screen, it's plainly visible (in the new Blu-Ray version) that a patch of extra carpet is under the edge of the seat. It was probably put there to level the seat or something. At the time, this was ignored, because on a standard SDTV screen, the edges are all rounded, so the very edge of the frame isn't normally visible.
Another thing that's plainly obvious in TNG's remastered version is all the black cardboard placed over the display screens in the back of the bridge, to block glare from lights. In SDTV, this wasn't noticeable because the quality was so bad.
Actually I would expect AI up scaling of SDTV in this case would perform better. It would assume semantically the props were real and would extrapolate them as such.
It's a widespread issue with the emulation of old games that have been made for really low resolution/different ratio screens and slow hardware, especially early 3D/2D combinations like Final Fantasy, and those that relied on janky analog video outputs to draw their effects.