(This is my view in the recent debate about posts giving a "rational" discussion of some random topic. It was originally at comment level but I've extended it and posted it in discussion because I want to know if and where people disagree with me, and for what reasons.)
I come to Less Wrong to learn about how to think and how to act effectively. I care about general algorithms that are useful for many problems, like "Hold off on proposing solutions" or "Habits are ingrained faster when you pay concious attention to your thoughts when you perform the action". These posts have very high value to me because they improve my effectiveness across a wide range of areas.
Another such technique is "Dissolving the question". Yvain's "Diseased thinking: dissolving questions about disease" is valuable as an exemplary performance of this technique. It adds to Eliezer's description of question-dissolving by giving a demonstration of its use on a real question. It's main value comes from this, anything I learnt about disease whilst reading it is just a bonus.
To quote badger in the recent thread "Rational Toothpaste: A Case Study"
I claim a post on "rational toothpaste buying" could be on-topic and useful, if correctly written to illustrate determining goals, assessing tradeoffs, and implementing the final conclusions. A post detailing the pros and cons of various toothpaste brands is for a dentistry or personal hygiene forum; a post about algorithms for how to determine the best brands or whether to do so at all is for a rationality forum.
But we don't need more than one or two such examples! Yvain's post about question-dissolving was the only such post I ever need to read.
Posts about toothpaste, house-buying, room-decoration, fashion, shaving or computer hardware only tell me about that particular thing. As good as many of them are they'll never be as useful as a post that teaches me a general method of thought applicable on many problems. And if I want to know about some particular topic I'll just look it up on Google, or go to a library.
It's not possible for LessWrong to give a rational treatment of every subject. There are just too many of them. Even if we did I wouldn't be able to carry all that info around in my head. That's why I need to learn general algorithms for producing rational decisions.
Even though badger makes it clear in the quote I gave that the post is supposed to about the algorithms used, the in the rest of the post almost all the discussion is on the object level (although the conclusion is good). That is, even though badger talks about which methods he's using and why, the focus is still on "What can these methods teach us about toothpaste?" and not "What can optimising toothpaste teach us about our methods?". I'd prefer it if posts tried to answer questions more like the latter. The comments exhibit the same phenomenon. Only one of the comments (kilobug's) is talking about the methods used. Most of the rest are actually talking about toothpaste.
So what I'm suggesting is that LessWrong posts (don't forget there's a whole internet to post things on) should focus on rationality. They can talk about other things too, but the question should always be "What can X teach us about rationality?" and not "What can rationality teach us about X?"
I simultaneously want to agree and disagree with your post. I, too, find LW useful for the reasons you laid out. I get a lot of value from posts the posts that teach question dissolving, righting wrong questions, holding off on proposing solutions, etc. I can take these skills and apply them to real world situations.
On the other hand, I'm not at the level where I can reliably apply these tools to the most important decisions I face in my life. There are some situations/choice that I need help from others to solve; I need help applying the instrumental rationality I learned from the aforementioned posts. I feel that posts on how to apply instrumental rationality can be germane to LW discourse. When I have done them, they have been very helpful. I've also gotten positive feedback from others.
Right now, I'm visually imagining of linear spectrum of possible LW posts. On the left end, there is the type of post you talked about, such as Yvain's diseased thinking. On the right end, there's completely unsuitable posts for LW. Porn, politics, etc. Between these two ends there is a vast span of posts that are germane to varying degrees.
Obviously (?), those on the right side of the spectrum I don't want to see at all on LW. Like you say, there's the whole wide internet to use. We need to help a well kept garden.
Maybe the "rational toothpaste thread" is only 60% appropriate for LW. (That's more or less a number I pulled out the air based on my feelings.) It's somewhere on the left side of the spectrum, but close to the center. I wouldn't want to see numerous posts like that all the time, but I don't mind seeing a few in discussion every once in a while.
More appropriate to LW is a post about applying instrumental rationality to choosing a major, college, or career. I'd say these questions fall between the left end of the spectrum and the "rational toothpaste" type threads. Unlike toothpaste, these are very important questions that are harder to solve than what toothpaste to buy. I would actually like to see a bit more of these.
So all that said, I think your criteria is too strict for my tastes. Yes, LW should definitely have a focus on learning epistemic/instrumental rationality. But I'd also like to posts on applying rationality to important topics. I think both can compliment each other nicely, and both are useful.
Edit: Just to be clear, the criteria I'm refering to is this: