A lot of Asian plants are invasive where I live. Although many of them are beautiful here, they do not always integrate in with the natural ecosystems in a healthy way. A major problem here in the mid-Atlantic U.S. is Japanese Knotweed, a beautiful (and edible) plant, which forms dense thickets shutting out the growth of native plants.
For this reason, I recommend people to exercise great caution when cultivating non-native plants. As beautiful as these plants are, they can wreak massive devastation to natural ecosystems, and in some cases, they can have immense economic costs as well (think of what Kudzu did to the south).
Many Asian plants have native analogues in North America. For example, there is a native version of pachysandra, Allegheny Pachysandra
which integrates well with the ecosystems in Pennsylvania. But, typically, the Japanese variety is planted. As most gardens who have planted it know, it can become somewhat of a pest, and is difficult to remove.
I think that a new sort of beauty is obtained when people replicate Asian styles of gardening using native analogues, rather than non-native plants. This can be a challenge, but it ultimately creates something new and beautiful, something that is in harmony with nature. Keep in mind that in Asian gardens, planted with native Asian plants, the plants are in harmony with nature. When planting these same plants in North America, the harmony is lost. In order to truly replicate the essence of these gardens, one must actually do a lot more work in locating the corresponding plants from our own wild ecosystems, and working to cultivate them.