Hi,
Note: I wouldn't recommend unlocking it above 60 based on what happend in skyrim when you did (the game became unstable).
It's quite possible what you're experiencing in Fallout4 above 60fps is instability which may result in a screen tearing look with screen play not meshing properly. As SinxarKnights explains it's a deliberate limitation of the game's engine and wouldn't be surprised if console/TV had an involvement in trying to make an advanced game run on a treadmill.
GTA 4's cut scenes had a similar effect on my 144Hz screen if fps were left uncapped since they were recorded in 30fps apparently, the characters would shudder quite badly being unbearable to watch. Capped at 60Fps was much an improvement but being a 144Hz monitor i couldn't use vsync i had to use Nvidia inspector to force it.
https://www.techspot.com/downloads/5077-nvidia-inspector.html
Give inspector a shot to force 60fps rather than rely on vsync. (If have Nvidia card) For AMD, not sure what is there for them, there's Radeonmod but not sure if its compatible with the latest offerings though.