I think it comes down to latency, or lag between pressing a button on the controller, and something happening. I guess some people may be less motion sick if the motion feels more "natural". But really it's just mostly just marketing.
TBH, I don't care either. Nor do I think that increased resolution is the be all and end all.
Digital Foundry did a good look at this when trying some old CRT monitors, wihch somewhat ironically don't have the same issues with resolution or refresh rates that modern monitors do:
I thought so to until I went to the cinema to view a movie, I would be bother by the lack of frames the first few minutes.
I can don't 'see' the difference between 30fps and 60fps, but I feel it. As 60fps feels way more smooth. But I adjust to 30fps after a while.
Response times I only notice if it's really bad, so I imagine the difference between ultra fast response times and 240Hz screens are harder to notice then a higher resolution, HDR or better in-game visuals.
The 120fps mode on the PS5 is probably for older 60fps games, like they do the 2x fps upgrade on the new XBox also.