Though this doesn't change the fact project itself is very useful and obviously it's her own personality problems rather than some conspiracy.
Real reason for that Kremlin action was funding of some politics-related book publishing and lectures. For non-profit "foreign agent" mark in practice bring regulation that almost impossible or too expensive to comply with. So Dmitry Zimin just decide to close non-profit.
Then most of people in Russian science community who still live and work in Russia have strong liberal views. Obviously they wasn't too happy about that since it's one one of few non profits in Russia that was actually funding science and education for real. Very few rich people in Russia ever donated anything to science or education so it's a big loss.
Elbakyan "nuanced standpoint" was such that Kremlin doing good job and since Sci-Hub users from Russia didn't agree she just decide to ban whole country.
Sci-hub is there to "expropriate the expropriators" in Lenin's words. That there is some wider benefit to the community is completely secondary.
While you can see my opinion on her personality above I still think you going into extremes regarding the project itself. Keep in mind that she is just end up being face of the project, but there more people working on it, and maintaining Library Genesis too, and dealing with risk of getting into prison for the service they provide to everyone.
So... one could go to prison for doing something that is explicitly illegal in most countries of the world, just so that the "face of the project" can preen about "standing up to the West", and fighting foreign enemies of the people, with the only risk to her being that Putin suddenly does a 180 and she's too slow on the uptake... Or one could, say, work on a viable long-term solution. Maybe setting up a wiki-like, peer-reviewed alternative publication scheme or something.
While the project does provide some benefit (which is not Elbakyan's goal), I just believe that the problem should be solved in an entirely different way -- you should start at the publishing side, not distribution side.
It's enough that few companies like Disney absolutely abused copyright. Yet we can live with it as long as it's just entertainment. Ok, they also put some horrible broken crap like DRM and DMCA and bunch of other things in our lives. Still it's not very important and might be after 10 years it's will be fixed somehow.
This is not the case for science. I can't even explain how wrong it could be to delay progress for years until "proper solution" is there. It's simply not acceptable. Sci-Hub might be illegal crutch, but it's important to have it.
I think good analogy for Sci-Hub would be Uber. It's might be absolutely hateful company for many here on HN that break every rule imaginable. Yet it's significally improved quality of life for millions of people and pushed taxi companies all around the globe to improve service.
PS: Also if you live in the US you might truly don't understand problems Sci-Hub solve, but there are people in ex-USSR who doing science on salary of $300 / month and they have no budget whatsoever on any papers. It's that bad. Yet some of these people still contribute.
I also don't think this is the case when ends justify the means. But stealing is much easier than trying to change copyright laws, let alone setting up a proper alternative publishing system, so there we have it.
As to why... I would hazard a guess that it's because she's neither a good person (far from it, by all indications) nor, really, a particularly bright one.
There's an example posted below of how she is a Putin stooge. Blocking access to everyone in your own country because scientists (you know, ones she is allegedly supposed to help) because the ones who are actually involved in science supported pretty much the only foundation that funds science in Russia when Putin decided to close it...
Sure, yeah, that's who selfless altruists working for the betterment of humanity do, not Kremlin trolls. (insert sarcasm tags appropriately).
Anyway, is there any proof that Sci-Hub is part of the Kremlbots, besides Alexandra Elbakyan being from Kazakhstan?