Batman is the main character in B vs S, and he got more positive reception than Superman did from people who didn't like how he was a killer. Everyone loved Affleck's performance. Before that Nolan gave him a huge boost with the Dark Knight trilogy so he could take time off and not miss a beat, that's something Superman hasn't got.
Its not about him not being an icon, its him having less attention than Batman and if that goes on for too long others will over take him. He was able to get away with that for a long time since only Batman and maybe Spider-man were moving in on his territory - now Iron man and Captain America are smelling blood in the water. He only keeps being relevant by constant relevant boosts, instead DC/WB's been doing weak attempts and relying on inertia. That's not going last forever. He's not in danger of being forgotten, he's in danger of being surpassed. Especially on the movie side. You know why people think Superman's a boring boy scout? Because Superman in the movies never left Reeves' shadow. Gal Gadot was able to do that with Wonder Woman, despite having a few appearances against Linda Carter, Cavill didn't do this when he was supposed to.