I don't think a compass is strictly necessary. Neither is a steel knife, signal mirror or a box of windproof matches. People did just fine without those modern amenities for many millenia... Apart from those unlucky ones that didn't. History is full of folks who met their sad demise because they weren't really equipped well enough to survive.

On a serious note, it is possible to get by most of the time without a map and compass. Terrain association, sun and stars, it's all good. That said, I would put a quality compass very high on my priority list when it comes to navigation in unknown, unfamiliar or generally difficult terrain.

Much of my hiking takes place in dense woodland where conspicuous landmarks are few and far between. I have a pretty good sense of direction and I don't get lost easily (knock on wood!)... But I'd be pretty embarassed to admit how many times checking my bearings with a compass saved me from taking a wrong turn, and possibly from a potential disaster on more than one occasion.

YMMV - but if you don't carry a compass out in the bush you'd better make sure to include a signal mirror in your kit indeed, you might be needing it more often than usual.