It is partly a matter of redundancy. Unthinkable as it might be, libraries do burn. They do have budget cuts. They get burglarized. Their archivists make mistakes. Better three universal libraries than two. Better four than three. When we're sure we have too many we'll deal with that; they are far easier to destroy than create.
It is true that things might be more efficient if everyone pooled resources and, say, kept track of the fact that we have ten distributed copies of Book X in the world but only three of Y, so we should be looking out for more copies of Y. Which brings us to a second reason to start a new public archive: as a pilot project to explore different ways of running public archives. Modern infotech is evolving fast; presumably there is lots of room to experiment with different strategies, and the national libraries have only so much budget for research.
Redundancy is why so much information survived from ancient times. When Rome collapsed, scholars elsewhere hung on to its knowledge and continued building on it while Europe pulled itself back together.
It is true that things might be more efficient if everyone pooled resources and, say, kept track of the fact that we have ten distributed copies of Book X in the world but only three of Y, so we should be looking out for more copies of Y. Which brings us to a second reason to start a new public archive: as a pilot project to explore different ways of running public archives. Modern infotech is evolving fast; presumably there is lots of room to experiment with different strategies, and the national libraries have only so much budget for research.