MSI: Use the dedicated backlit button on your keyboard or utilize the SteelSeries Engine or MSI Center software. Dell: Press F10, Fn+F10, Fn+F6, Fn+F5, or Fn+Right Arrow keys. So in other words your mouse isn't sophisticated enough to implement the behavior of shutting down the LED when it's not in use. On gaming models, use the Fn+Up Arrow key. (A really useful behavior would be, when the mouse is powered up, to flash the LED several times to indicate 'I have power and have started up!' and then turn it off if there is no communication with a host.) The LED being on would confirm that the host is interacting with the mouse, not only providing power. This feature could have diagnostic value also. (There may even be other ways in the USB protocol to infer that the host is down.) So the mouse should be able to notice that it has not been polled by the host for some time, and shut down the LED. It contains a little microcontroller which coordinates all of its functions, including USB communication with the host. The mouse is a little computer in itself.
The LED being on provides no benefit, and can be a nuisance at night. After all, the mouse can't be used when the computer is powered off. But that's not a good answer why it is on. The LED is able to stay on because the mouse is powered, yes.
