This is one of those things were it doesn't matter for every game or every genre. But for games that move very fast and require the combination of fast reactions and accuracy -- specifically, FPS games -- high refresh rates matter a lot. For many other genres, it simply makes the overall experience more pleasant, but not so much so that you can't do without higher refresh rates. Nobody is missing not having 150fps on Civilization V or plodding games like God of War, but you'd appreciate it in GTAV or League of Legends, and you'd be at a measurable disadvantage without the highest refresh rates you can have in something like competitive Destiny 2, CSGo, etc.It sounds nice but I'm more than happy with 1080p 60. If I get to the point where I can budget more money into PC hardware I might pick up a high refresh monitor, but there's also ray tracing to consider.
Growing up playing dos games on the family PC getting 1 fps at times on certain titles will always stick with me. It's hard for me to not be happy with what I have now.