The term y'all are looking for is 'remaster', the sort of in-between of re-release and remake. A re-release is the original game with next-to-no improvements or new features; the standard is typically fixing framerate issues and making the game widescreen, but those are by no means very prevalent. Most really older games, say pre-Dreamcast, just get a straight re-release on a digital platform. A remake is a total ground-up project made from scratch with modern hardware and sensibilities in mind. A remaster is when you release the old game with a handful of tweaks not found in the original, but the game is still largely the same.
Take Jet Set Radio HD vs. Sonic Adventure 2 HD. SA2 was a straight re-release of the Gamecube remaster, providing no new features or tweaks, and not even bundling the exclusive Gamecube content with the game, you gotta buy that separately. JSR HD provided the (almost) full soundtrack, a documentary, camera control, new graffiti, framerate fixes, unlockable tracks, and after its release, faster load times.
So, with all that said, I agree a Shenmue remaster is definitely doable and would be fantastic. Tweaking the controls to allow for better dual-analog support (though d-pad and analog stick worked well for the Xbox version of Shenmue II), widescreen, maybe adding support for Japanese audio and English subtitles for both games, easy cross-save, 5.1 surround, and tweaks to Shenmue I brought over from Shenmue II. Those are what I would want the most out of a remaster, nothing /especially/ fancy. Hell, just asking for more than a straight, vanilla re-release of Shenmue on modern platforms seems a bit greedy at this point.
