Why had nobody in the League of Shadows told the public who Batman was in the first place?

The implicit answer here, which is supported by the comic book lore behind Batman’s relationship with the League of Shadows, is that Ra’s al Ghul, founder and leader of the League, will not allow his operatives to use this tactic. I can think of the following three reasons:
1. Honor: Despite their unsavory methods, the League of Shadows does abide by a warrior’s discipline and code of honor, similar to that of the samurai, as evidenced by the training depicted in the movie (I trust you can find the scenes). I’d also note that the League and Ra’s are unique among Batman’s rogues gallery, in that they are terrorists with a political agenda (ecological preservation), not psychopaths (in their mission statement at least, individually they certainly are), which furthers the argument that they aspire towards some vague ideal of honor. I’d consider this a minor reason, but also an essential one to understanding the League as a symbol of Batman’s own warped sense of justice and honor, taken to an extreme.
2. Empathy: I believe that Ra’s empathizes with Bruce Wayne’s obsession/passion for crimefighting and strongly approves of his methods, other than his refusal to kill. Essentially, Batman uses terror and darkness to his advantage in the same way that the League does. Revealing his secret identity would violate that kinship. Throughout the Nolan trilogy, Ra’s seems to identify with Bruce (this is very obvious because Liam Neeson has his “kind face” on, not his “I will find you” face) and essentially believes that if he continues to be Batman, he’ll eventually give in to the dark side and join the League — destroying the Batman identity would delay that. Ra’s hopes that eventually Bruce will see the light (or more accurately, the lack thereof in his hopeless mission to end crime) and join Ra’s in creating a better, less-populated world as the son he never had , which leads smoothly into the final and strongest reason.
3. Love: Although it’s not clearly depicted in the latest movies, Ra’s al Ghul has one of the most epic man-crushes in all of comic-book history on Bruce Wayne / Batman, or “The Detective,” the naughty pet name he most prefers. As the peak example of all that a human being can possibly become, Batman is, in al Ghul’s eyes, the only man worthy of succeeding him as leader of the League of Shadows. In the comic book lore, he continually pushes his daughter Talia to seduce Bruce and give birth to the perfect heir (hinted at in The Dark Knight Rises). As I mentioned before, Batman reminds Ra’s of himself — driven, gifted, sociopathic — and, as a true narcissist, Ra’s can’t help but fall madly in love with him. So there’s your answer: Ra’s (and subsequently Talia) al Ghul protects Batman’s secret identity because he loves him.
Post-coital PROOF:

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