They're still, to this day, very important, and the fact that they're dying is a bad thing.
And to address your second paragraph, libraries have been, some more slowly than others, adapting with the times. My local library system has _three times_ the number of ebooks as they do print books. They provide access to things like EBSCOHost. Heck, the librarians in this system are even trained to help you find jobs.
In fact, all of this was addressed in the article.
It also seems obvious that instead of access to libraries a better use of money would be access to the internet. SpaceX and Facebook are already working on solving this problem. It’s just a matter of technology and infrastructure. If it’s unfeasible to lay wires in remote areas maybe access to internet would better be served by satellites or balloons.
If a person is not educating themselves through the internet what makes you think they would educate themselves at a library? At some point it comes down to personal responsibility and as much money you throw at the problem it will never solve it.
Libraries should evolve with the change of technology and move their function from curation and access to information to something that is able to benefit more people. Books occupy volume and removing them would make more room for desks and rooms where people with no access to quiet areas could use to be more productive.