I do get your point. I'm not suggesting that framerate should't matter to you, it just doesn't matter as much to me and many others. I also make a valid point that as resolution goes up, the need for higher framerate goes up, which means that I can personally be satisfied with 60 fps on a 1080p display, whereas I can actually see the "stutter" on a 4K display at 60 fps, especially during panning (due to the image having to jump across pixels when framerate is low).That's all well and good, regarding the image quality and HDR and colour gamut etc.
But none of that will win you a clutch last-second peek-a-boo gunfight when it's double OT and you have your rank to play for. A fast display with a GPU driving high frame rates and consistent low frametimes will.*
*player skill notwithstanding, of course. You get my point.
All that said, I am fairly confident that this Stadia device will not be marketed to competitive eSport champions, LOL
Speaking of, I'm assuming your competitive gameplay is happening on a LAN, because Internet latency will far outweigh any benefit you would get from a 240Hz display, unless all your friends are connected to the same ISP via fiber (and even then you get router latency not found on a LAN). And for anyone thinking this is off-topic, you'll note my first post is all about the LATENCY of this Stadia device being the true enemy of its success.