"I think we'd probably see that the internet is a far more sustainable, cheaper medium through which to transfer information."
Absolutely true. Yet not that relevant. Data transfer cost isn't a major factor.
The journals in my fields are all electronic. They no longer have paper distributions. As a result, the library no longer needs to store a physical copy, and people can retrieve a copy from their office instead of spending the hour to so to find it in the library and photocopy it.
Great savings, right?
This also means that the publisher, as copyright holder, can enforce access restrictions. For example, I (as the member of the public) can use the chemistry library of a large university about an hour away to get online access to some of these journals, without paying an extra fee. However, I am not allowed to print or make copies of these articles. Once upon a time, when everything was in paper, there was no way for the publisher to make that restriction. Precisely because information transfer is cheaper, it's now possible for the publisher to have more fine-grained control.
As a result, ILL services have gotten worse. The rise of internet-based document retrieval services with limits on public (non-student/non-staff) access has meant that modern library users may need to travel more now, in order to visit a library with a given journal subscription, than 25 years ago, when an ILL request would have been possible.
See http://www.spiegel.de/international/zeitgeist/how-copyright-... for "The Digital Paradox: How Copyright Laws Keep E-Books Locked Up." Quoting from it:
> If a student in Freiburg wants to read the hard-copy version of a book from the university library in Basel, he or she can simply order it via an interlibrary loan. But if only an electronic version is available, interlibrary loans are generally not an option. The student has no choice but to climb into a train and head to Switzerland to read the book on a university computer.
This sounds like the European version of the scenario you presented, only it was solved with the 'quite dated' ILL system, and exists with e-books.
In passing you highlighted the underlying reason. The publishing companies would like it if the laws and technology were set up so that making a copy of a journal article at a library is "piracy" (I prefer the term 'copyright infringement'), unless they get paid for making the copy, and they as copyright holders should be in charge of determining what the price is. (The ILL system addressed copyright payments through RAND-like copyright clearance agreements.)
Technology which makes it easier for copyright holders to control their copyright makes it harder for people to use the same materials. Either worthy people without the funds can't get access to a paper or there is 'rampant piracy'.