ABS is like fuel injection in that people dislike it for no good reason. People have an "I'd rather have a carb you can tune" over having fuel injection. Simple fact is fuel injection works better, and very, VERY few people can properly tune a carburetor. Same with ABS. In a slippery condition you can't modulate the brakes like ABS, and like mentioned before, you can't ease braking pressure on just one wheel.
What kind of example are you looking for? ABS has worked for me a number of times in the winter, and on loose gravel. Once, I wasn't paying attention on the way home from work, and didn't realize the car in front of me had stopped. I slammed on the brakes, and ended up about 3 inches from his bumper. I am sure had I not had ABS I would have slid. I've also needed it on steep hills. One in particular where the townships change, and they will stop the salt/cinders mid hill.
I drove a car (moms old 95 Blazer) that had a perpetually bad ABS system. It was terrible. This is what you are experiencing, I assume. If it doesn't work, it sucks. But that doesn't take away the usefulness of a working system.