Answering the question "Why is Sci-Hub so popular?":

Because it works. It delivers information and knowledge to those who need it.

Because information and knowledge are public goods. As CUNY/GC says, an "increasingly unpopular idea",1,2,3 but an absolutely correct one.

Because it democratises information.

Because much the world cannot afford to pay US/EU/JP/AU prices for content. Including many of those in the US/EU/JP/AU. And most certainly virtually all outside. Billions and billions of people.

Because the research is (often) publicly funded, conducted in public institutions, and meant for the public.

Because information and markets simply don't work.
https://redd.it/2vm2da

Deadweight losses from restricted access and perverse incentives for publication both taint the system.

Because much the content, EVERYTHING published before 1962, would have been public domain under the copyright law in force at the time, and much up through 1976 and the retrospective extensions of copyright it, and multiple subsequent copyright acts, have created.

Because 30% profit margins are excessive by any measure. Greed, in this case, is not good.

Because the interfaces to existing systems, a patchwork fragment of poorly administered, poorly designed, limited-access, and all partial systems are frankly far more tedious to navigate than Sci-Hub: Submit DOI or URL, get paper.

Because unaffiliated independent research is a thing.

Because the old regime is absolutely unsustainable. It will die. It is dying as we write this.

Because the roles of financing research and publication need not parallel the activity of accessing content. Ronald Coase's "Theory of the Firm" (1937, ), a paper which should be public domain today under the law in which it was created and published, and should have been by 1991 at the latest, but isn't, tells us why: transactions themselves have costs.
http://sci-hub.ac/http://papers.ssrn.com/sol3/papers.cfm?abs...

Because journals no longer serve a primary role as publishers of academic material, but as gatekeepers over academic professional advancement. This perpetrates multiple pathologies: papers don't advance knowledge, academics are blackmailed into the system, and access to knowledge is curtailed

Because what the academic publishing industry calls "theft" the world calls "research".

Notes

See GC Presents, "At the Graduate Center, we believe knowledge is a public good. This idea inspires our research, teaching, and public events. We invite you to join us for timely discussions, diverse cultural perspectives, and thought-provoking ideas."
https://www.gc.cuny.edu/Public-Programming/GC-Presents

See GC President Chase F. Robinson, introducing a conversation between Paul Krugman and Olivier Blanchard. A rare moment where the introduction itself contains some provocative thoughts. At about 50s into the video. (The remaining 72 minutes and 20 seconds aren't bad either if you're interested in discussions of global economics.)
https://www.youtube.com/watch?v=zndOEQnMC44

Joseph Stiglitz, "Knowledge as a Global Public Good," in Global Public Goods: International Cooperation in the 21st Century, Inge Kaul, Isabelle Grunberg, Marc A. Stern (eds.), United Nations Development Programme, New York: Oxford University Press, 1999, pp. 308-325.
http://s1.downloadmienphi.net/file/downloadfile6/151/1384343...

https://www.reddit.com/r/dredmorbius/comments/4p2rwk/what_th...

(This has proved to be among my more popular articles, including being picked up by the Open Access community.)