Certainly there is no right or wrong answer here, but I can not imagine going into the backcountry without a compass and map.
I carry a Brunton 9020G baseplate, a Garmin 301, and a Casio altimeter watch. The latter two have electronic compasses. The weight of all three is 177grams.
Most common use of a compass for me is with the Casio, deciding which fork of the trail to take when under the canopy. Frequently maps here are way out of date.. do I take the fork to the NW or the one to the NNW? Also, in heavily forested areas or in a sawanobori canyon, a GPS and terrain association sometimes do not work.
"..if you carry a GPS you should also carry a compass as back-up, but than if you take only a map and a compass, than you should also back up those, so why not take an additional compass?"
A GPS, compass, and electronic compass use different principles of operation. So in my opinion they are complementary, not redundant. But then I am 'light', not SUL. And I err on the side of caution since I hike with novices for whom I am responsible. I can teach the use of all three different devices, time permitting.