I care more about the vertical inversion than the horizontal one. Not certain why. Have played with horizontal inversion on before and it didn't bother me much after a minute or two.

Not necessarily, IMO. You tilt your head back to look up, but you don't tilt your head left to look right.

I think it's an issue of mapping potentially 6 axes of movement to a 2D plane. They don't all line up the same way. Left and right in the game line up with left and right on the mousepad, but up and down in the game map to forward and back with the mouse.

Thinking of the mouse being glued to the top of your head works better for me.

No because when you look left your head doesn't tilt right. When you look up your head tilts backwards