I don't want that when we go to Buddhism and we has no or less choice but to choose Japan Kii Mountains which is only a national level or Taishan for Taoism. WHS also really lack of sites with the Hajj in Saudi Arabia or great Hindu pilgrimage sites which seem more attractive for the little Green Man.
I don't fully understand your point, Durian. You are right that the WH list is low on non-Christian pilgrimage sites. But we have to make do with what's on the WH List. Kii Mountains and Taishan seem OK to me. For Hinduism we could choose Pashupatinath (Kathmandu) and the Chola Temples (see http://www.worldheritagesite.org/tags/tag984.html).
We'll see when we get there (and have to remember to include pilgrimage sites).