From observation of where people are, where they hike and where emergencies tend to happen I suspect that most people could get along with a very simple compass.
or even no compass at all, provided one has an adequate topo map. Hiking in the mountainous western US, mostly in Arizona, I used my compass exactly twice for real in thirty years of active hiking, climbing and SAR work. Both times were in foggy, restricted visibility situations.
Coming to coastal California and getting on the water, I have used the compass a lot more. I remember vividly one day paddle when I mounted my compass on my sea kayak mainly to show what a cool dude I was. We launched, got just out of the breakers, and the fog moved in. I must have referred to that compass at least 100 times over the next ninety minutes as we crept toward our destination.
Even in mountain country, I religiously carry a decent compass (Silva Ranger). It isn't very heavy, and when you need it, you really need it.