There’s also confusion over human response time vs whether you can perceive something. Even if 240Hz looks slightly different, if a human can’t react to that difference (other than to say it looks nicer, which is a personal preference rather than an empirical assessment of “better”) then it doesn’t really matter anyway. Kind of like how Avatar looked different in 48Hz instead of 24Hz, and at the time it was hailed as some revolution in movies, and then it came and went. Personal preference.
As a direct answer to your question, I was a gamedev from 2005 to 2012, and back then people were arguing that 120Hz couldn’t make a difference and that 60Hz was fine. It stuck with me, since it seemed mistaken. So I shouldn’t have said “generally accepted,” just “I vaguely remember the world arguing a decade or so ago that 60Hz was good enough in all situations, e.g. competitive gaming.”