The infrastructure is gone, but with the knowledge still available (10% of 6 billion is 600 million after all!) they will rebuild communities in a few decades and be back to a larger nation/state status in a century.
I guess I'm a bit more pessimistic on this point.
It's my feeling- really, that
is all it is- that people rely a bit more on books & other data storage media today than they realize.
Even with 600M people surviving the initial onslaught, you still have to have the right mix of survivors in any given area. You need people with proper smithing skills, for instance. Once a relatively common profession, the blacksmith (the craftsman who makes all tools) has largely been replaced by the industrial factory worker, at least in most First World nations.
You travel to developing countries, and you have a different story. In an interview in the 1990s, the leader of a Middle Eastern nation once mocked UN sanctions & boycotts, pointing out that what the world was denying his country were goods they had only had access to for 40 years.
And it is precisely the world powers' population centers & military installations that would be most heavily targeted by the Illithids...meaning survivor distribution would be "lumpy" and uneven.
I think I'm going to start a related thread on this...
On stuff surviving...
It depends. <snip many good examples>
I understand that books are wonderful ways to concentrate knowledge, and that just a few surviving tomes could provide a great kickstart to the rebuilding process...
This is one of the reasons I chose the meteoric strike as the method of Illithid-induced ELE.
After suviving the initial onslaught, there is going to be a severe temp drop due to the ejecta from the impact craters. Like the citizens in Asimov's
Nightfall, people will be looking for anything they can get their hands on to keep warm, and paper products are going to be among the first things to dissapear. Even if there are books out there in the countryside, survivors who know their ecosystems will probably burn pre-cut wood first (from their woodpiles), then less valuable paper products (newspapers, magazines, reciepts) & other superfluous burnables. Depending upon the length of the meteoric winter, eventually, they'd have to choose between live trees and dead-tree products.
My personal guess- Bibles & similar religious tomes would be among the last to go (not only might some be more religious minded after an apocalypse, typically, such tomes are informal resources for family records), right after manuals on maintaining important equipment & D.I.Y. books. Encyclopedias would also be among the last to go...but actual engineering texts?
From-scratch find-the-materials-mine-the-materials-refine-the-materials-make-the-tools-make-the-machines type manuals? Given the choice between heat & that kind of book...
Like some of my world's inhabitants, you live in an island chain. People there will probably survive with much more of their infrastructure intact, if for no other reason than most islands have an import-based economy. They may be nearly self-sufficient for food, but they must import most fuel, tech, and raw materials (like most of the industrial metals) from elsewhere. Islands would simply be low priority targets, and would probably experience more damage from tsunamis than anything else.