120 Hz can also noticeably improve frame pacing for 24p video*.
120 Hz vs 144 Hz? Barely noticeable when flipping between the two. Not sure if I'd pass an ABX test with 100% accuracy.
Can't speak for 240 Hz or higher, as I haven't used them.
* Though 119.88 Hz is probably a better default for this since most non-DCI "24p" video is still 23.976 FPS; this is changing, but until browsers and streaming apps support VRR for video, I'm not convinced this is a good thing due to the mountain of legacy 23.976 FPS content.