Even before the Overlords came to Earth, the sovereign state was dying. They have merely hastened its end: no one can save it now--and no one should try.
This quote is said by Stormgren, in Chapter 3. It makes plain an important idea in Childhood's End: that the Overlords, while certainly speeding up the process, have not done anything that humanity would not have eventually done itself. The existence of sovereign states, Stormgren knows, are the main source of conflict in the world.