Shape of structuring elements for morphological gradients
I looked up in Jaehne, Gonzalez, Soille (the one you've posted as well as Mathematical Morphology and Its Applications to Image and Signal Processing) and some other special morphological papers and haven't found neither any design criteria for the structuring element nor any special hints why it has to be symmetrical.

Personally I think that a symmetrical SE is good for the same symmetrical effects on the object you want to modify.
With my existing experience I would not use a non-symmetrical SE, because I can't take it for any object or scenario and I don't know how it will react for other cases.

Nevertheless it's an interesting question and I am trying to get an answer.