The point of the lesson should be the same as every lesson. Make you a better pilot.
After this lesson, I have learned that I should never turn on a GPS, or land if I don't know where I am or what events cause half my plane to become in-operational. I should fly around until I figure it out.
Didn't know that was going to make me a better pilot.
I wouldn't make that argument... the point of the flight lesson, and the (intended if not apparent) point that most of the "old crusts" are making here, is that such an exercise just makes you a more challenged student. Obviously, it'd be crazy to expect you to use DR and pilotage from a completely disoriented standpoint with the same accuracy as GPS. But forcing a student to
try makes for a nav-muscle-building exercise that is useful in the long run. To me, "better pilot" means "more well-rounded pilot." I am not an old crust, studied under pretty young crusts for the most part, and had ground-based navaids and a little basic GPS and LORAN at my disposal when learning to navigate... but the focus was always on the basics first, the nice-to-haves after. It's not a matter of yearning for the past... most old crusts know life was not really better "back in the day"; they just remember it fondly because they were young then.
I'm not that old yet, and I already catch myself doing it. When you are old and youngsters freak out that you actually were allowed at one time to fly an airplane that did not have its own autonomous cybernetic brain, using only Earth satellites for navigation, you will understand, too.
So when those of us who learned to fly back in the caveman days grumble at the new breed's frustration with old-school nav skills, keep that in mind.
You cited a radius, based on time and known airspeed, after a bunch of random heading changes. Okay, that's actually a lot of information, provided you have a chart, and part of the circle lies on the chart. Stuck with only that, you are in pretty good shape, really. You probably won't have to search even 5% of that circle to find something outside that you can identify on the chart, at which time you are no longer lost.
Assuming suitable vis, pilotage is usually pretty damn easy. The cost of learning to use it is negligible in light of its potential value. Sure, while searching for something, you might bust an airspace, or go somewhere you would just prefer not to be. But this sort of thing still happens, with alarming frequency, even with the very latest toys available, in good working order. Pilots also fly into terrain and each other with terrain and traffic alert technology. Don't ask me why, I don't know. But I bring that up to point out that you are really not any more likely to do that while using only compass, clock and chart, or maybe one VOR radial, than you are while using a GPS-based device. I really don't think so, based on my experience (which is modest, but pretty well-rounded).
You also mentioned feeling that everyone's saying anything other than looking at the chart is going to fail you. I don't get that from this discussion, but I will say that compass, clock and chart are probably the
least likely things to fail you. They are harder to use with great efficiency, downright primitive compared to GPS, but they are usually enough, and very unlikely to be un-usable or contain errors unknown to the user, as is often the case with any radio navaid (including GPS).
Personally, I place compass, clock and chart at the bottom of my nav-tool pyramid; they are the foundation. If I'm using something else, even just NDBs, I make sure the "three Cs" are there, ready, and I don't completely ignore them when I'm using something else. The simple reason is that I know they are least likely to let me down... BUT I have to be proficient with them, or they will be useless.