Don't confuse throughout and latency. The mouse may be measuring and sending data every 1-2ms, but that doesn't say anything about the latency before the data is handled.
This is also a pretty important point: most monitors refresh at 60hz anyway even if your game seems to be measuring much higher framerates, so there's a worst case floor of ~17s on just visuals lagging behind input because you're waiting for the next screen refresh anyway.
The mouse measuring data every 1-2ms will increase the quality of the motion tracking, but it won't necessarily help you with latency unless the data gets to the game fast and the game handles the data quickly.
True, though these days 144Hz monitors are everywhere (Personally I used a CRT until LCDs were capable of 120Hz, not sure I could ever go back to 60), makes a big difference I think when down to a 7ms window. Using a mouse at 125 on a modern screen feels really janky.
