Yes, movies should allow significant changes to national monuments. Cinema has no more claim to reality than novels or comics do. In fiction, a world similar to our own confronts us. Fiction gives us the possibility of seeing our world in foreign or other-worldly terms. Our familiar reality and history suddenly becomes unrecognizable. However, this experience allows us to reconceive the world and to meditate on so-called "possible worlds." Through fiction, we imagine that our reality is susceptible to alterations and changes. This is especially true of national monuments which citizens of a nation collectively share. If plot in cinema alters a national monument in order to surprise, scare or throw off the audience , why should we reject this effect that could ultimately lead us to reflect and consider images, such as national monuments, often taken for granted?
If a larger Statue of Liberty will make a more dramatic and involving scene, then I think it is the right choice for the movie. Cloverfield and other films are not educational materials. They are entertainment. The creators have no responsibility to maintain accuracy in matters regarding geography, monuments or anything else.
Movie makers should be able to do just about whatever they want, creatively, in their films. Restricting the way they can represent national monuments sounds like something that would happen in North Korea. Freedom of expression and freedom of speech are beautiful things that we can't take for granted. We may not like everything that people say or portray in films, but we need to respect their right to express it, or we're on the path to a totalitarian state.
Movies should be allowed to make big changes to national monuments. For instance, the movie "Cloverfield" showed the Statue of Liberty's head as larger than life. This is part of artistic license. Most people realize that a movie is fiction and should not be taken literally. Movie have a right to take these liberties.