Well, in many ways Quora (just like any other web platform) IS a private communications network.
And their mission is certainly not to "share and grow the world's knowledge". As with any company, their mission is first and foremost to make their investors happy, mostly by striving to make them richer every day than they were the day before. The dreamy tagline is just a way to make the pill more appealing to swallow for the users.
(remember Google's "Don't be evil"?)
I also despise Quora, and used to think it was terrible that huge swaths of human knowledge would be lost a few years from now when they inevitably get acquired/go bankrupt/etc.
But I'm not losing sleep over it anymore: they will be a mere blip in the history of human knowledge, and while some valuable chunks of knowledge will be lost, we can't do much about it.
I do wish the Wikimedia foundation set up an open Quora alternative. Wikipedia is about objective knowledge - it seems like there would be a place for a counterpart project about subjective knowledge. Properly moderated, it could be really, really interesting.