Actually, libraries seem to be ahead of the curve in terms of the economy. They’re one of the few industries that already seems to require at least one PhD (preferably more than one) for an entry-level minimum-wage job. 
But seriously, more information means that we need more people to work with it. Not just because of the 'net. We now have repeated copyright extensions, DRM shenanigans, a shift to centralized streaming sources for media (from which things may vanish at any time), and consumer devices from which the manufacturers may arbitrarily delete data without the owner’s permission.
The librarians and archivists may become our only hope, as things in all forms of media now tend to go out of print and vanish from the culture long before copyright expires. If that trend continues, soon librarians will be the only ones who can help you find something older than two weeks (that isn’t public domain, (cc), or pirated).
And with control of media being so centralized, suppression or surreptitious revision (Ministry of Truth style) becomes an actual possibility. We’ll need people who know about and can access the unedited/unsuppressed versions.
I grew up in the old days and learned to find things in the card catalog and/or by browsing the shelves. The few times I asked a librarian about something, they basically just pointed me to the card catalog or the shelves, so I might’ve thought the same.
But since then, I’ve encountered plenty of instances where I’m searching for A while what I really want to find is C but I don’t know that I don’t know about the missing link B (or don’t even know that C exists); or I’m finding lots of things, but not what I’m looking for because I don’t know the right way to narrow down to a specific in some topic I’m not familiar with. As long as our brains don’t know that they don’t know what they don’t know, there’ll be a place for people to help.
