This is definitely something that could use attention I believe. I was moving it off screen too, but then sometimes it would end up hovering over some instrument in my cockpit and give the pop up readings as I turned my head. Highly annoying.
The F10 thing is working out better for me, as I don't actually use the virtual cockpit much once I'm actually flying, but it does get wonky when I bump my mouse. It would just be a lot better if it just hid the pointer, which is a pretty standard thing really and I'm surprised it doesn't do this now.