While I like this premise and I agree that Batman does demonstrate a real-world problem solving approach as opposed to say Superman, I am not certain we can hold Batman up as the standard for real-life problem solving. I understand the argument. Superman has powers beyond human ability, Green Lantern holds a magic ring. These are not examples of real world problem solving. Batman has to function as a regular human and therefore has to solve human problems. However, Batman is also Bruce Wayne, billionaire. He has money, time and gadgets-a-plenty. According to the comics, Batman is also a well-read genius who knows a remarkable amount of facts and is an expert in a myriad of skills, including martial arts and fencing. He has his own plane which he can fly himself. He can afford to sleep all day and be up all night or jet off to Europe for three days with no questions asked. While Batman is a good example of someone who must solve problems without magic or alien powers, he is not an "every man" type of character.
If we are going to look for a comic book hero to represent the common man, I prefer Spider-Man. The Spider-Man from the original comics, more so than the recent movies, was an everyday guy. Peter Parker had to make ends meet as a freelance photojournalist while also saving the world, yes with certain superhuman powers, but he was an average guy trying to work two low-paying jobs while also finding time for a social life.
All of that said, I think it is important to point out that no comic book hero is truly an example of good, real-life, problem solving skills. In the real world, if we have a problem to solve, most of us can't throw Bruce Wayne's money at it, nor can we wait for it in an alley down the street and beat it about the head and shoulders with our fists.
Comic books and movies provide an escape from reality. They provide a world where the hero always wins, the bullies and bad guys always get what's coming to them and problems can all be solved by the application of maximum effort and outstanding moral fiber. That's why we run to those worlds after a hard day of reality. Let's leave Batman and the others in that realm we escape to. There's no reason to bring comic heroes into the harsh reality of our world.