That’s one of the biggest issues with rendering older games in higher resolutions: the artwork/design and poly count were balanced around what the hardware was capable of spitting out at the time, as well as the display technology.
Blowing that up to HD often nets unflattering results, a bit like watching a theatre performance very close up. You quickly notice all the imperfections and tricks that were never meant to be seen, gaps your imagination would have filled in.
So developers often face a dilemma when correcting for this in HD remasters and the like. In the case of Twilight Princess they made a decision to upgrade the texturework, since the original textures would look extremely unflattering at 1080p. But now the game has taken on an inconsistent appearance, its razor-sharp textures at odds with the now-angular (at 1080p!) low-poly scenery.
And then there is the concern already brought up about how the atmosphere of the game is just different once you sharpen the look of it by presenting it in higher resolution, while also removing some visual effects which don’t play well with a crisper image.
An example off the top of my head would be the image quality of Tales of Symphonia (Retro AV |OT| RGB, CRTs, Upscalers, and more - #1558 by poptart). It really doesn’t tick the box as far as HD as a marketing device is concerned, so the PS3 version removed the depth of field, exposing the low quality (by HD standards) assets for what they were. The move to widescreen was also handled inelegantly, the developers zooming in all scenes.