Great thread, Thanatos. I've meditated on the story of the Gordian Knot a number of times, and am glad to see I'm not the only one.
I find something incredibly refreshing about going into a situation where disputants are endlessly locking horns as they sweat small details, and just disrespecting all the subtle layers of complexity by cutting through with a simple and inelegant solution. Unfortunately, opportunities for being a real-life Leroy Jenkins are few and far between, but they bring home an important point: just because an issue in our world is relevant and divisive, doesn't mean a detailed analysis or a complicated way of modeling it are helpful for solving it. In other words, if your goal in thinking about a problem is to find a practical solution, beware overthinking it, because you may miss the simple and obvious solution right in front of you. As anyone in either IT or medicine (among other fields) knows, when someone presents a problem to you, rule out the simple problems with simple fixes first, if you want to use your resources efficiently. There's no point taking off the case to a computer tower if the reason it won't turn on is that it isn't plugged in. There's no point performing CPR on a comatose ER patient, if a drop of blood from his finger indicates that an ampule of dextrose would perk him right up.
Problems that are thought or talked about simply as thought experiments, for the purpose of imparting to the thinkers / debaters a realization about the human condition, are another story. This is typical of all the "hard questions" of philosophy -- it would appear that a lot of these issues never get settled once and for all, no matter how fine-toothed a comb is used to go over them, or how long they're debated, with each side becoming ever more nuanced and voluminous in their case for why their viewpoint might very well be right. Eventually you have to just stop and take a stand, and then get back to more practical and mundane matters. And this is the lesson imparted, I feel, by debating the hard philosophical questions: in the end, it's entirely up to you to decide what answers to life you find convincing, and no one can do that for you. And in some cases, when approaching some tough questions about life, you just might find a quick and dirty tentative solution (and subsequently leaving the debate alone, or "cutting" out of it, if you will

) serves you just fine.