Are there quantifiable benefits to using a frame rate higher than a multiplayer games server tick rate?

First thing first, not every game server runs on 60 tickrate, Valorant runs on 128, CSGO private tournaments run on 128 tickrate, but anyway, the fact that the server is not responding you with the same low response time as your monitor doesn't mean that you don't get any advantage in having a 144hz or a 240hz monitor.

Higher refresh rates mean lower input lag, so the game will read your input sooner, you will see animations smoother (easier to see if an enemy is using a certain ability in Overwatch, Paladins, Sekiro...), you will be able to track moving target WAY easier because you will get more information to your eyes in the same time interval and you will be able to move your mouse and having quicker response time from the monitor if you have to correct the point you are aiming at. It applies to any other game too, "not fighting games, because they are often hard-capped at 60 FPS". In Rocket League, with lower monitor response time, you will be able to turn your car and correct your air or ground trajectory sooner. I switched from 60hz to 144hz last year and I saw quantifiable benefits in any game I tried without hard-capped fps. BO4 was way easier, I was more competitive in R6, I was more precise with car movement and shots in Rocket League. If you are not yet sure, this page says that 96% of R6 pros (real pros) use a monitor capable of displaying at least 144 FPS per second. I mean, they probably have a reason to do so.