But then you must be sacrificing small, precise movements. Assuming your monitor is 1920 pixels across, and your mouse's DPI is high enough, you'd need to move your mouse 1/1280 inches (or approximately 20μm) to move the cursor a single pixel. How does your hand physically move 20μm? If your 1.5 inches of movement spans a 4K monitor, then you need to move your mouse 10μm to move the cursor a single pixel.

EDIT: babypuncher's reply seems to address this using on-the-fly DPI adjustment. Pretty cool!