>Plus, it misses the point: in the event of something able to take out something crucial to the entire US library system for any appreciable length of time, the librarians themselves would most likely have far more pressing concerns in their hands. And that would be our new single point of failure.
I'm not exactly sure if I'm following you, but the general idea of this kind of "resilience" is to introduce enough safety / backup measures at all points in the society so that there is less things that hinge on "single point of failure".
The scenario I had in mind was a national grid of a much smaller country going down. (Apparently bringing up all the power plants back online is not as straightforward operation as flipping some switches 'on'.) For example, in conjunction with other crisis (say, conventional war with cyberattack component) that would turn out to taking much longer than anticipated (because aren't they all "over by Christmas"), so there might be an adversary interested in keeping it down.
And the libraries are not the only institutions handling critical data that used to be stored on paper but now exist on computers. The particular solution of retaining backup paper card system might be silly or otherwise prove infeasible at closer inspection, but what kind of backup systems the current institutions have?
edit. Looking at the rest of the comments, smkellat might have provided a splendidly simple answer upthread. At least, concerning libraries.