We've already gotten reports about how this is a sort of hypothetical question which invites a lot of speculation about the answer...but for my own specialty, pulp history, I can already say that the Internet Archive is a tremendous resource, and if it continues it may well become essential.

There are two parts to this. The first is the Wayback Machine: copies of old web pages, archived for when those sites go down and are no longer accessible. A lot of resources in the early internet, established during the 1990s, are no longer accessible anywhere except through the Wayback Machine...and that includes the emergence of some important authors and the publication of some notable books and scholarship during the time period. Without the Wayback Machine, that material would almost assuredly be inaccessible: it is not in print, it was never in print, it probably never will be in print.

The second part is access to works that are in the public domain, which is an ongoing process. Many pulp magazines are now in the public domain in the United States and other countries due to various copyright laws, and dedicated scanners and uploaders are putting them on the Internet Archive - which is terrific because pulps are inherently fragile. The cheap paper literally eats itself, becoming brittle and falling apart, eating itself from within. In as little as sixty years, there might not be any pulps remaining except digital copies, even with the best efforts of some libraries to preserve physical copies.

And I want to stress: being able to digitally search many of these issues is a godsend. I have a shelf full of old fan-made bibliographies which I can page through in an effort to find what I'm looking for, but they only point me in the general direction of an issue, story, or author - actually reading an issue of an old pulp, seeing it in the context it was published in with all the ads, art, and editorial commentary - just adds tremendously to the information I can glean from that source.

That said, limitations: the Internet Archive might not be around forever. I doubt it's going away anytime soon, but it's not an institution like the British Library or the Library of Congress; it is also more dependent on donations rather than government funding or an endowment. It is much more open for anyone to upload material, the constituent materials are very diverse and not always well-curated (although this is getting better all the time), but you skirt the Wikipedia issue where sometimes a group of well-meaning amateurs trying to groupsource solutions doesn't lend itself to the same kind of intelligent organization and focused curation that you might get from library science professionals.