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.
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).
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.