... we will usually need to make a full 180 degree of turn in a reverse turn to keep moving in a straight line down the floor,
I think you will find that if you turn 180 degrees on a Reverse Turn, you will continue against LOD, and not be very popular!
Otherwise, I agree: the cross allows a freedom to make the turn - I think of it very much as a latin "volta" type movement, and the position for man on 3 is not very different (dare I say) from a latin cross. Don't forget that lady doesn't cross until 6.