Just tuck the mouse away in the lower left or right corner as you start every sortie.
That does not work when I need the mouse to move the map around or adjust other settings from the clipboard. And it's a pain to do it when I'm trying to fly and fight.
I understand this can be worked around, but it's a computer, why should I have to do the work? As for the whole "center of the monitor" thing, why not ask for a separate feature that optionally puts a small mark / crosshair / customizable bitmap at the center of the screen if that's really desirable?