Well this might sound harsh but ehh… if you went for a 360Hz monitor and you seek to only play demanding games… you will also require a beefy PC out of the box… so you would also require at least SLI RTX 3090 that allows for most games to be played at 200 fps on a 1080p.
But this also involves how good the devs are with optimizing their game and allowing the components to run that much fps
I bought a 240HZ monitor cause i was into eSports and i was making money for a brief period… but now its kinda like a curse cause i can only now play the games like these on at least 120 fps with either VSYNC or GSYNC turned on to kinda give false positive of high fps… aka to not make it feel stuttery…

