The only time I use a middle setting is on my 5.5-22 NXS. At 11x, I can still use the reticle sub-tensions to measure stuff (multiply x2). The only times I've done it have been while fall bear hunting. I like to set up with the sun in my face, because the bears stay out longer in the shade. The lower power really helps when the sun is pounding into the objective from a low angle!
The other times the scope is powered down is with a new shooter. Until your natural point of aim is mastered, it can be difficult to acquire a small target at distance with a 22x scope. I teach finding the target at 11x, building the position correctly, then zooming in for a precise aiming point.
Of course, all of this is from a long range hunter's point of view. When still hunting with "normal" range scopes, the power is at the lowest magnification. I don't ever remember using a middle setting on any of these.