Why do higher frame rates require lower resolution?
I am not an engineer, but I think you've answered your own question. 

This is a bit of an oversimplification, but if t is the time it takes to record, process and store a pixel from a frame consisting of p pixels, then 1/(t * p) is your maximum frame rate. So if you increase the framerate above the maximum you need to decrease either t or p. And since t is fixed you have to decrease p - the number of pixels.