Should libraries even attempt to catalog exhaustively the web in a manner parallel to print publications?

An alternate view sees web information as fundamentally different from print publications:

I want my students to use the web for what it was first designed to do -- to allow an individual user to connect with other people, and with their fluid, developing ideas. Printed material is still the best place for well-formed and clearly articulated ideas. But on the web, you can find ideas in motion, and you can communicate far more easily with the people who produced the printed material than was possible before we all went on line. (cite)

While some web pages are clearly the electronic equivalent of printed texts, many others contain evolving material that should either not be catalogued or that call for fundamentally different approaches to cataloguing.

Alexa Internet is one project that attempts to archive the entire contents of the web by archiving bi-monthly snapshots onto magnetic tape. In only its third year of operation, the archive is reported to contain 13 terabytes (the Library of Congress is reported to hold the equivalent of 20 terabytes). (cite)