They learned from it, they just learned the wrong lessons. Nolan's approach worked wonders for Batman but Snyder coming in and trying to ape that approach with the rest of the DC stable was a mistake.
I think they focused on the thing that was easiest to replicate (it being dark and serious), but they seemed to totally missed the fact that this approach specifically worked for the character of Batman, as you say, who's always been very malleable in this way.
They had a tonal mismatch right from the beginning IMO. MoS never really achieves the pseudo-realism tone it's going for because it's an over the top alien invasion story with tons of CGI that ends up feeling more like a video game by the end. They also didn't give their universe much room to grow in terms of stakes since the very first movie already deals with an Earth-wide threat.
Most of all though it feels like they made the mistake of assuming TDKT's success was due solely to being "dark", forgetting that those are very well-made films that told good stories. The pseudo-realism allowed a wide audience to really invest in the stakes and root for Bruce Wayne (who was portrayed as a flawed but
likable character) on his epic, heroic journey to save Gotham. The movies were faithful to the core ideas of the source material without being slavish to every little minute detail, and as a result they were able to connect with a huge audience while being a fresh, interesting interpretation of the mythos for the fans. I felt with BvS and fear with JL that we're using fanservice to attempt and paper over the cracks. While that might be enough for a lot of fans, that is never going to be enough to get those better reviews everyone seems to desperately want.
I also think one lesson they clearly missed was how powerful it can be to see just hero develop across a series of films when it's done well, with a vision. Hopefully they'll go back to focusing on the solo films after JL. Every indication at this point is that they'll be doing just that, which is fine by me.
