As someone who reads a fair number of papers, I definitely feel like the publishers' days are numbered, and not just because of Sci-Hub and LibGen. More and more often now, I can find papers that I want, legally, on the first try. Even more encouraging, I find that when I can't find a paper I often just have to wait a few months and try again to find an open Internet source.
Case in point: a few months ago I wanted this paper -- http://bit.ly/2tE4O4K -- but all the CiteSeerX links were broken and apparently had been for a long while. About two months later it's back. This is just one example, but I find this increasingly works with many papers.
There is also ResearchGate, which is a social network to get papers from an authors, which is legal if they are alive. But their sign-up process is also much harder for independent researchers. You have to "prove you are a researcher," as though attempting to get access to research papers weren't prima facie evidence of that.
In CS the worst paywaller is consistently the ACM.