These very 'Asics-like' running shoes are making a huge come back as seen in Raf Simons AW12 and SS13(runway pic). Apparently this is a very 'deliberate' effort of mixing sports and fashion. Raf has done this before. I remember there was one season with bright fluorescent colors. With thick padding and jaggedness at the sole area, perhaps they are very comfortable to wear, and thick soles are good for walking on wet surfaces.
UPDATE: Colette now carries the green versions, hi and low. I keep asking myself whether I will ever want to wear such shoes, hmmm.