So I get this question sometimes. Here's my answer.
The library does make its resources available on the Internet. All you need to do is use our databases or if you are not affiliated with the university, you can get access through your local public library.
The library has a public institution, democratic mandate to make its resources available to all people. This is not true of for-profit companies, like Google, who have no ethical responsibility at all or legal mandate to provide you access to information.
When you find a good academic information on the Internet, it's because a library or a similar nonprofit institution put it there. Google didn't put it there.
You cannot depend on random people to post resources on the web. First, they could take it down, die, or very likely do not own the copyright and will be forced to take the material down. Besides, random people more than likely do not own the back issues of important academic journals or rare historical material.
It's a really bad idea to digitize everything and then destroy the physical copies. First of all, overcentralization leads to the risk of unforeseen system failure. Then you have the risk of
cyber-terrorism. Finally you have the risk that powerful forces decide to alter the historic or scholarly record in ways that will be undetectable to many people. Or god forbid choose to destroy the cultural record of the people, as has been done many times throughout history.
Finally, print will always be relevant. Internet-based databases are a wonderful finding tool. But computer screens are not conducive to high level thinking and reflection. When's the last time you spent more than 20 minutes reading something on a computer screen line by line? Print and literacy produce higher-level abstract thinking and higher cognitive function.