Sometimes it would be nice to be able to force lines or labels to appear in front, even though they are "physically" behind other objects. In this diagram I achieved this effect by shifting the surfaces directly away from the camera so that they were secretly behind their outlines, but that is a hack and would not have worked with a perspective projection.
Here's a simpler example in which it might be desirable to see the complete equator without the added complexity of a translucent surface:
settings.outformat = "pdf";
settings.render = 4;
import three;
unitsize(4cm);
draw(unitsphere, white);
draw(path3(unitcircle));
Incidentally, the layer() command does not seem to do anything useful in this context.