It works well enough over a reasonably short duration, it doesn't work very well near sunrise/sunset. During the middle part of the day (say 10a-2p) I can be confident that if I'm walking into my shadow that I'm heading approximately north--not perfect but good enough that for gross navigation I'm not going to bother to pull out my phone and look at the map. (I would never be out in the wilderness without *having* map/GPS/satellite texting/headlamp, but that doesn't mean I always *use* them.)

Of course, on a small enough area, short enough time, and rough enough goal, it's fine. The same applies to the earth being round or flat. I don't compensate for the curvature of the earth when figuring out area of bricks for a front walk, or building a shed. So what?

With your example, if I'm just trying to walk roughly north in the middle of the day and I know that my destination is just west of mountain slope that I'll see when I get near, then it'll work to just keep our shadows roughly in front of us. But, let's take finding a point on a functionally featureless plain or desert. It's 8 miles away, due North, so a bit over a two hour brisk walk. Local noon (w/DST) is 12:45, so we start at 11:45, and the sun's azimuth is 154°. By the time we get close-ish two hours later (say 7mi at 3.5mph), the sun's azimuth is 207°. So, we started out walking North, but we've been bending to the East, and are now off course by 53° to the East, and our average path is 26° off. After 2 hours at 3.5mph, we should be 1 mile away, due South, and set to arrive in 17 minutes more walking. Instead, we're 3.2 miles away from our objective, and walking 53° in the wrong direction.

The zone where this works is really pretty small, and we're probably using landmarks instead. And if you're trying to do this on water without compensating for the earth's rotation, you'll soon be in trouble...

It's not nearly that bad. You start heading too far east and bend back. After your two hours you are exactly on the right direction but have gone a bit farther than you needed to and are 26 degrees off course. I've never encountered any large, featureless terrain; rarely am I moving in a direction that's not either with the nature of the terrain or nearly directly across the terrain--it's easier to go a bit farther while minimizing the terrain fighting.

>> You start heading too far east and bend back. >> rarely am I moving in a direction that's not either with the nature of the terrain or nearly directly across the terrain

Right, you are not ONLY following the sun's direction, you are compensating for it's motion over time, and using the terrain as a guide.

This is exactly my point: we cannot do what GP stated and use only the uncompensated sun's angle as a guide, save for very brief trips. And most of those we're also using landmarks to compensate.