The Library of Congress is the "Great Library" of our time. It was designed as such, because it serves the Congress, President, and other leaders of the United States.
Early on, it was "seeded" with the entire personal library of (former) President Thomas Jefferson. Thereafter, it had a mandate to acquire two copies of every book published in the United States. Even if another national library has such a mandate, their economies, and hence their publications would be smaller.
After World War II, America made great efforts to "digitize" and "internationalize" the Library of Congress, probably more than any other country in the world. Basically, the Library of Congress defines "national book" more broadly than most. And even if "other" libraries may have had more resources "up to World War II or so," it's been 75 years since then, with that period covering the "American century."