Japan's
Ise Grand Shrine is both very old (having been established sometime between 4BCE and the 5th century) and very new; every 20 years, the shrine buildings at Naikū and Gekū
are demolished and rebuilt. This symbolises the Shinto teachings of the cycle of death and renewal in nature and the impermanence of all things, and also serves to pass on the crafts and techniques used to build the shrine. In this case, one could say that destroying the artefact keeps the institution alive.
Also, the Japanese notion of originality of buildings (a building is original if it's built according to the original plans in the original location) prevents them from losing as many "original" architectural artefacts permanently. As a child of the information age, I find this notion quite sensible.
Now when I think of it, maybe Americans should just rebuild the WTC and put a commemorative plate there saying "these buildings were knocked off in 2001, rebuilt in 2013".