Stack Exchange is the best Q&A on the Internet, and I see you've picked up on that:
The format of these Stack Exchange sites might be the best of the Q&A's I've ever seen, so why not create a General one?
Now, the question is, why? Why is Stack Exchange the best Q&A on the Internet? To answer this, one might look at Yahoo Answers, which lets people ask whatever they want about any topic, and people can answer any way they want, up to and including posting low quality content that doesn't even begin to answer the question. This is why whenever we Google anything of importance, Yahoo Answers isn't at the top of the list.
Stack Exchange wins because it focuses on experts, and like AsheeshR mentions, you can't have experts without focus on a very specific topic and attracting a core base of users that will serve as defenders of the site's overall mission and quality.
A general, catch-all site would be impossible to maintain, and such a site would tarnish Stack Exchange's reputation.