Snowden gave proof and technical details about what was happening. It is like showing proof that Israel has nuclear weapons. Israel doesn't talk about it, they may or may not have nuclear weapons, most people think they do, and such a revelation won't surprise anyone, but it is still a big deal, because they can't use their "deliberate ambiguity" strategy anymore.
(Speaking only for myself; I didn't work on any of this directly)
Not to mention the whistleblowing on the Trailblazer Project and New York Times reporting on the "Terrorist Surveillance Program" in 2005/2006.
When the Snowden leaks came out it was not a surprise. Granted most people don't go out drinking with the people doing the spying, but even people who work at the NSA can't keep a secret, if it was even meant to be a secret.
I think the lesson here is that a "conspiracy" can exist as long as all of its participants believe they are morally in the right. The people involved in the NSA dragnet believed in the cause; when a non-believer (Snowden) got involved, the gig was up.
It's easy to believe that a government agency would overstep its bounds to spy on people it (according to complex laws that well-meaning people misunderstand or disagree with) shouldn't. It's much, much less credible that a large number of US government employees conspired to, say, bomb the world trade center. A conspiracy like that would quickly enlist someone with moral qualms about it, and it just takes one to blow the whistle.
Most criminal conspiracies succeed as evidenced by the fact that most crimes aren't solved and most criminals aren't arrested. In fact, the larger your criminal organization, the less likely you are to go to prison. If I shot a passerby on the street, witnesses would be coming out of the woodwork. Friends or family would identify me by surveillance tape or report my strange behavior. Conversely, if a gang in Baltimore kills some guy, nobody will come forward. Let's not even get started on cartels.
Instead, I think it's much more apt to say that whether or not a conspiracy will be betrayed depends a lot on what will happen to the traitor/whistleblower.
If you want to turn in an evil, murderous, criminal organization, you'd better be willing to die or flee somewhere beyond their grasp. That bravery needs to be combined with an ability to get compelling evidence to the people who need to see it.
Also, not all of those 10k people might not be knowing what they are doing or don't care. You can cloak a lot of espionage activity with forms, sheets, memos, brainwashing and what not.
A lot of people in the intelligence community were aware but few had all the details or would care to look
So maybe not in the widespread public awareness, but if you were Googling trying to answer the question, "Is the USA gov't eavesdropping on all communication traffic?" in 2013 pre-Snowden, then the reasonable conclusion would've been, "Yes".
The 2006 lawsuit was about AT&T cooperating with the NSA to facilitate tapping their customers, quite different from the NSA surreptitiously digging up and tapping private fiber.
Illegal domestic electronic espionage/surveillance wasn't a vast secret. It was widely known that the Feds were making every effort they could to push down that road, and the Feds had a very long history of illegal domestic espionage. Frankly, it was obvious that it was going on. A lot of people I know in tech had crossed paths with other people that knew pieces of the puzzle, that some domestic espionage programs were going on (particularly supercharged after 9/11). You'd get snippets of it in discussions. Snowden's revelations were not the first, it was the bombshell that was comprehensive (and only for a small part of what they were doing).
It wasn't yet proven, and the full extent wasn't yet known, there wasn't enough credible public evidence to demonstrate exactly what they were doing. There's a huge difference between something not being secret, and being proven, and that's what Snowden's actions helped to correct.
While it's in the not-yet-proven stage, the malevolent skeptics in particular will all sandbag any attempt to reveal it, by burying discussions under conspiracy tags and swat away any attempts to dig into what's really going on. Some skeptics do that on purpose because they have a vested interest in doing so, some do that because they're cowards (which is what is represented by the common statement: "if you don't have anything to hide, you don't have anything to fear" - it's cowardly people hiding from a moment of confrontation).
Ready for another one? They're still performing illegal domestic electronic surveillance. That too isn't some vast secret. Oh I know, but but but they're not supposed to be doing that! Golly.
For sure it's true that a secret can be kept by three people if two of them are dead. But there are clear cases where large groups of people have been able to keep secrets as well, or at least keep them from spilling out into public awareness.
I'd bet that for most crimes, the secret isn't kept, and there is someone else out there that knows who did it, who simply doesn't tell law enforcement. And yet most serious crimes aren't solved.
Humans have a real need to tell other people personal things, even to their own detriment. But sometimes things stay secrets even if tons of people know about them.