The idea behind Cooking.Stackexchange, as with all Stackexchange sites, is indeed to become a repository of information - not a forum where people ask the same question over and over again, but a compendium of questions and their answers, where people look up their problem before asking again.
(Excurstion: This is by the way why we are so strict about rules like "all new posts have to address the question exactly", "questions have to be clearly defined" and similar. They are totally against the unwritten rules of human conversation, and new users have difficulty getting accustomed to them, but they ensure that the previously-discussed information can be found - as opposed to forums, where the information about the correct internal temperature of fish might be hidden in a topic about the preferred pan types for fish.)
That being said, it is unlikely that the world will ever run out of questions to ask. Stack Overflow is at 12 million questions and hundreds of new ones come in every day. We are several orders of magnitude smaller, but a dearth of questions is nowhere in sight.
As for the traffic "shifting" from active community to search engine traffic, that cannot happen, because this is how we have been from the beginning (except maybe the very first days of beta). I just went to our questions, ordered them by age and looked at roughly the median. First, the median is from Oct 2014, which shows you that we have been growing (the site is 6.5 years old but the median of all questions is at 2 years in the past). Second, I averaged the statistics of 5 questions on top of the page. These questions had a total of 8 answers (including a deleted one), 13 comments, and 10735 page views. The number of people who just come here to read the questions and never interact (in fact, never register) has always been higher than the number of people who interact.
This is also how Stack Exchange wants it to be. You don't make a successful site with 200 enthusiasts, of whom 15 are active daily; you make it with millions of people coming for good content. That's why many of the other rules are created such that, if there is a conflict of interest between the OP and the anonymous reader from the Internet, the policy usually resolves in favor of the anonymous reader.
This is quite surprising for people new to a community, especially those coming from forums which where not so strongly moderated. Note that Stack Exchange is not claiming that this is the single best way to run an online community - but it is the way that made them what they are, and they are staying with their model.
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