For as much as I loved Quake 3 - and Quake Live, for that matter - I'd be lying if I said I hadn't had my fill. If they remastered it, I'd jump in for a couple of bouts and then be done with it. I'm not sure it could hold my attention like it used to, and I doubt a remaster would bring back the MP scene.
Quake 4 is a solid little title, but frankly, it's still really sharp so I'm not actually sure what a remaster would do except ultra-wide support, soft shadows, and higher quality textures. Maybe that and a console release would be enough? I replayed it a few years back and was surprised that it held up as well as it did. id tech was just that far ahead that even older tech games are still really solid today. I ended up finishing it.
Personally, I'd love a DOOM 3 remaster, one that undoes the butchery of the BFG Edition. Clean up the texture work, put the flashlight mechanic back, fix the display ratio non-sense, re-tune the weapons and enemies, and add proper soft shadows; DOOM 3 as it was intended. But there's plenty of mods that do all that, so not sure it's worth Night Dive's time.
Curious, at least.