IMO it already has. How many people can actually see a difference between 240hz and 120? I can barely see the difference between 60 and 120, and I have damn good eyes.

How many people's reaction speeds are fast enough for the fraction of a second to matter competitively? Human reaction times are typically around a fifth of a second. The difference between a hundred-twentieth and a two-hundred-fortieth is pretty damned negligible in that context.

Obviously it matters to professionals, because a couple of milliseconds can mean thousands of dollars, but they're both at the peak of human ability and often playing in-person. If you're online, your internet connection is doing a hell of a lot worse to your latency than anything your damn monitor is doing.