The fat tires really smooth out the ride on rough surfaces. I've never had a bike with suspension so I can't compare the two. They are also very stable at low speed, which is practical in some situations and a desirable feature for people who prefer a leisurely pace. I don't see them being a fad, a niche yes, but they are here to stay.
They take a lot of the drama out of riding rough terrain increasing accessibility for people without super fast reflexes.