If the need is for basic land navigation, how necessary is any compass? My take is that a compass is rarely necessary, absent foggy/cloudy conditions or navigating at sea.

The vast majority of my experience has been in the topographic feature bountiful western US. Here you orient yourself and/or the map by aligning the terrain features and proceed up or down the ridge or canyon, heading for the peak, pass, or valley. I have gone weeks without referencing the compass. If you are operating in flat, featureless terrain or thick forest, it may be a different story. At sea, a compass is frequently used, at least pre-GPS.