Video needs to catch up to higher refresh rates, but there are also those of us who regularly watch videos at 2x or higher speeds, so there is that edge case where a 60hz video can benefit from a 120hz monitor
Yes. And 1000Hz lets you get reasonable frame pacing even at non-integer multiples of 60fps.
video is typically way less than 120 Hz for sure. There are ways to get your PC video player to increase / motion interpolate your video (similar to how some TVs do it and everything somehow looks like an old soap opera). I myself have found it to work via potplayer with "avisynth processing" enabled plus various tweaks you have to lookup (reddit thread somewhere) to make it work -- presumably it would crank to 1000 hz but never tried.