The game is no where near optimized to run on 120 fps. The papyrus engine (skyrim game engine) will fail because it has to calculate vertexes of meshes too fast for it to handle. Yes you can change the settings and yes it will run on 120 fps and higher but you will be damaging the code of your papyrus engine irreversibly and no amount of high end pc specs will change what will eventually happen. It's not a matter of if it will happen, it's a matter of when will it happen.

That being said i am not just going rain on your parade, i suggest you reinstall a backup of the game every 20ish hours of gameplay and you'll be able to play on 120 and higher fps. This should help with the longevity of it but that's depends on what gets corrupted and if it is saving process all your saves can be corrupted to a point where you can't realistically repair them. So for this you need to create copies of your saves that are in your skyrim's document save folder and put them somewhere else so that in case that happens you lose a hour of gameplay maybe one quest instead of every save file. Now all of this can be automated all you need is a code at a specific set time to reinstall the game engine and relevant files, your mods and to make copies of your skyrim save folder. Which tbh can be done by a text document saved as a .bak you manually run or a coding software like python. Of course you are free not to do this and this is not even full proof but it's better in the long run.