I agree that everyone ought to deeply think about deep questions at least long enough to come up with answers or have a satisfactory explanation of why no answers are there. But you only need to go through this process once. After you have the answers to these questions, there's no call to continue thinking at this level unless you come to believe that the answers you found are wrong.
In short, there's no reason to go seeking new deep answers unless you have reason to think your deep answers don't work for you as well as they could. As I implied in my sanity line point, developing a sense of when that is happening is a valuable skill that most people simply don't have. But meta-level thinking doesn't develop that skill.
One of the sharpest and most important tools in the LessWrong cognitive toolkit is the idea of going meta, also called seeking whence or jumping out of the system, all terms crafted by Douglas Hofstadter. Though popularized by Hofstadter and repeatedly emphasized by Eliezer in posts like "Lost Purposes" and "Taboo Your Words", Wikipedia indicates that similar ideas have been around in philosophy since at least Anaximander in the form of the Principle of Sufficient Reason (PSR). I think it'd be only appropriate to seek whence this idea of seeking whence, taking a history of ideas perspective. I'd also like analyses of where the theme shows up and why it's appealing and so on, since again it seems pretty important to LessWrong epistemology. Topics that I'd like to see discussed are: