The advantages of this approach - occlusion and view-dependent lighting - are undermined by the fact that too much of the colour depth is sacrificed to hitting the necessary framerate. The sort of simple scenes it can display could be displayed better by a swept volume.
Most of the time we don't move our heads up and down very much, so the lack of vertical parallax seemed like it wouldn't be a big limitation. But one of the situations where we do move our heads quite a lot is when presented with a neat little 3D effect sitting on a desk.