Interestingly, this very question follows the same mold: it presupposes that Quora has failed :)
They were clear in the early days that they were following the model of "build a huge audience, then monetize in some way we'll figure out later". They succeeded at the former, and they're still floundering at the latter.
I'd accept the OP's premise that it failed at making a ton of money. As for whether it failed at its user's goals ... that's harder to say.
That's not scalable.
Asking the crowd for answers and having the crowd vote on the answers is not epistemologically sound. That is, it doesn't produce correct answers.
It's fine if you want to express yourself on a topic like "Did Tom Brady win all those Superbowls or did Bill Belichick win them?" (what answer could be better than watching the Patriots play the Buccaneers?) or "What IDE do you like for Javascript?" but you can't get to Heaven or even The Truth that way.
After that, there were a lot of people willing to write informative and entertaining content. (Caveat: I am one of those people who was reasonably popular at that time, so take that perspective into account.) That helped them do a lot of good SEO.
Unfortunately, that was as far as their plan took them. They had the eyeballs, and surely it was going to be Facebook all over again. But FB has the draw of a constant stream of your friends, and they weren't going to muscle in on that. Twitter has -- honestly, I have zero idea what it is people see in Twitter, but whatever it is, Quora didn't have it.
Maybe it's what you said. You can't Q&A with celebrities, but you can listen to them spew a constant stream of inanities.
They certainly didn't care about The Truth. They hoped for entertainment. And they got it; they actually did, a lot of the time. But it turns out that there just wasn't a lot of money in it.