This, of course, presumes libraries are also mostly gone, since you don't need WikiPedia if you have a library.
The premise isn't that the folks with WikiPedia can rebuild modern society. It's that they literally can't (even if they had better knowledge resources), but would still have a survival advantage from having a little bit of the old knowledge. The fact is that if we lose our modern society, we'll never be able to build it up again. We've dug up all of the easily accessible resources, already. Scavenging from the good old days is the best any post-apocalyptic society can hope for, as bleak as that sounds.
¹ I vaguely recall Wikipedia already provides some way to download all pages in bulk, but I can't seem to find it (if it even exists anymore, or if it ever actually existed instead of me just hallucinating it)
I have libraries and WikiPedia is still pretty useful. Searchability and portability / mobility would be pretty valuable attributes in this type of scenario.
In general, the scenario is, that the whole world is broken down, but full of tech.
So many machines to get back to working. Machines beat muscle on a scale
Most robotics don't work in areas of heavy radiation, because radiation damages electronics.
Even chat is possible for example between two buildings where radio might not penetrate the walls. But sure, at that point if you can lay down cables, then it's simpler to just build a telephone.