Given perfect eye tracking, that could work for the vestibulo-ocular reflex case where the eye counter-rotates to keep the world stable during head rotation, also given that no object is close enough for the parallax from the eye moving in space during head rotstion to be noticable.

It would not fix smooth persuit tracking of a moving object while the head is stationary though, as you could not selectively shift the moving object to match eye rotation while also keeping the background stationary.