FAQ
You should only ask
non-trivial, answerable questions that demand expertise in our site's subject.
Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page.
The current FAQ standard, while quantifiable, depends entirely on the judgement of the asker. Long experience suggests that once a person asks a question on a Stack Exchange site, they are no longer unbiased about it. Therefore, it's not very helpful to ask them if it's an actual problem that they face; people will go to great lengths to post-justify a question once asked.
Besides, motivation isn't really the problem here. The problem is described in the second sentence: bad questions displace good ones. In truth, whether the asker is sincere hardly matters compared to whether the question does a good job engaging the sorts of people who provide excellent answers. Simply having a problem is no guarantee that your question will be interesting. Homework questions tend to be poor even though they are "practical, answerable questions based on actual problems that you face" because they are often trivial for experts.
Before Philosophy.SE was allowed to go into public beta, we had to answer what our site was about. As Paul Graham points out, the entire field has been dominated by "the exploration of knowledge that has no practical use." (As it happens, I disagree with most of that essay, but it does seem true that as soon as a bit of philosophical knowledge becomes practical, philosophers loose interest in it.) So how do you test if an asker is sincerely asking a question and if the answers will actually matter to them? Rather than psychoanalyzing the user, we decided to focus on "domain knowledge".
The question of motivation is pretty well addressed a little later anyway. ("If your motivation for asking the question is...") What makes a Q&A site useful is a group of "experts" who are willing to watch the questions and provide reliable answers. Asking impractical questions on SO risks driving off the folks who answer questions there because SO is about practical programming. People answering questions on philosophy are ambivalent about practicality, but care deeply that questions somehow engage the existing literature. In both cases, questions that don't demand the sort of skills and knowledge that experts have obtained are likely to be a distraction to the core contributors of a site.
About
Get expert answers to detailed questions
Focus on questions you've seriously pondered. Include details about what you have already learned and what you are trying to find out. Putting more thought into questions before you ask will help you get better answers.
The about page is focused more on guiding new users, so instead of focusing on why the policy protects the site, we should try to persuade them to ask good questions for their own good. I picked the reason that is perhaps the most general. But there are plenty of reasons for asking well-specified questions:
You might find your own answer and not need to ask. (Or better: self-answer.)
Understanding your own question helps you understand the answers.
Upvotes.
But hopefully, the proposed text will help askers reorient themselves toward asking questions for the sake of learning from the answers.
Summary
Rather than make the requirement contingent on the asker, point out that people shouldn't ask questions that are boring to an expert.