As you can see in the original Reddit thread, the people who claims their card have died have all throughout gameplay, not primarily in the menu. It's the high FPS which people think is abnormal which has led people to thinking it's dangerous, even though it's not.
High FPS in menus, loading screens etc. has been normal since the late 90s.
I mean no disrespect here, but if you knew how GPUs were programmed, you wouldn't even propose this idea. Rendering works by submitting a queue of commands to a driver, which in turn translates it into the GPU's native API. The GPU is in control over frame rate and potential frame pacing. A rendering engine submits new commands as soon as the driver accepts it, and is unaware whether the command is executed or if the GPU just accepts more commands. If you e.g. have V-sync enabled, the renderer will stall when it calls to swap buffers, until the driver detects the GPU is done. Attempting to time rendering from the rendering engine will be much more crude, as it has no direct control over when the frame is actually rendered. This is how games and thousands of programming examples works. Attempts to add sleeps or wait-loops in the rendering engine will be a very imprecise way to reduce frame rate, and is likely to cause stutter and input lag in a menu.
Whenever you see people claiming high FPS is dangerous, that a game needs to regulate power or balance the GPU, or even regulate the clock speed of the GPU, it's a clear sign they don't know what they're talking about.