if your videocard can not push out the refresh rate on the monitor, the high refresh rate is pointless.
Example A.
You got a pathetic IGP which can only push out 27fps on a 120hz 4k.
This is a complete waste of that panel, because technically your only pushing out 27hz refresh rate.
So in that explaination, you are not even pushing the monitor anywhere what its capable of.
Example B.
You got a glorified RTX 4090 pushing 500 fps on counter strike source.
You have a glorified samsung neo G8 pushing 240hz.
In this case your videocard is so massively overpowered, it will drive the full potential of your panel.
Given your panel will only display 240fps out of the 500 your videocard is pushing, things like Gsync or Freesync will rate limit the card to match the panel so tearing does not occur.
In Example B, you have the proper setup, while in Example A, you will have a bad experience especially with the tearing and stuttering you will notice from the low fps.
Ideally you want to pair your max FPS ability on your vide card with the appropriate panel.
So if your card can not drive whatever your trying to drive at 60fps, you probably to stay with a 60hz monitor, unless you intend to upgrade to a faster gpu somewhere in the future, or your a competitive FPS player, and play with low settings to try to get the highest fps possible.