I've prepared a large number of National Register of Historic Places nominations. There is nothing in these designations that prevent an owner from tearing down a building which was found to be significant enough to be included in the registry. That is left up to the owners conscience. I suppose if they were proud of their community they wouldn't do it. It is a honor to own such a place.
I don't live in Anchorage but I got to watch the original "Star Wars" movie there in 1977. To be honest I think I was more impressed by the theater than by the film. Hate to see it fall victim to the "malling" of Anchorage.