Let me stress that I am not talking about web sites in general but rather am talking specifically about sites that depend on quality unpaid contributions from a large numbers of people.
>building a big successful company at scale is rarely done without taking on external investment.
Wikipedia is a counterexample. According to Alexa, Wikipedia is the sixth most visited web site in the world. But more to the point, no VC-funded or stock-market-funded company I know of is foolish enough to try to compete with Wikipedia. I think that fifteen years from now, we will see a similar situation among Q-and-A sites -- at least those where the answers are contributed by unpaid users. In other words, I predict that Quora -- as well as Stack Exchange, which has also taken VC funding -- will be eclipsed within 15 years by sites not funded by VC or other profit-motivated investment.
Any competition for Google Search is likely to come from companies like Apple or Microsoft that already have plenty of money to pay engineers or from investor-funded for-profit companies. That is because the "non-profit sector" is unlikely to be able to summon up enough skilled labor or funding to compete with Google Search.
In contrast, setting up a competitor to Quora or Stack Exchange is relatively easy (especially since these new entrants can learn from Experts Exchange, Stack Exchange and Quora), and going the non-profit route (or the for-profit "lifestyle business" route without external funding) does not alienate a large fraction of potential unpaid contributors.