Because the "delayed" or real input does not correspond to the image you see on the screen. That's why FG is most useful when you already have high base framerate as the input gets significantly lower and the discrepancy between the felt input and perceived image narrows.

Example:

30FPS is 33.3ms frame to frame latency (+ something extra from mouse to displayed image for input)

With 2x FG you get at most 60FPS assuming there's no performance penalty for FG. So you see 16.6ms + mouse to display frame to frame but input remains 33.3ms + mouse to display.

Same from base 60FPS 16.6ms to FG 120FPS 8.3ms perceived but 16.6ms+

Same from 120FPS 8.3ms base to FG 240FPS 4.15ms perceived...

As you can see the difference in input gets smaller and smaller between base FPS and FG FPS as you're increasing the base framerate.

This is however a perfect scenario that does not represent real world cases. Usually your base FPS fluctuates due to CPU and GPU intensive scenes. And during those flucfuations you will get big inpuy delay spikes that can be felt a lot as they suddenly widen the range between perceived image and real input... Couple that with the fact that FG almost always has a performance penalty as it puts more strain on the GPU so your base framerate and therefore input will be automatically higher.