But the thing is, a story "about" Robin is still a story about Batman. Just like TDK will have a Joker that plays a major part, often upstaging Batman as he usually does, it's still about Batman. It's always about how these supporting characters are viewed through Batman's world; how they impact him and vice versa. How they reflect his inner struggles. He's a very introverted character; we need these more flamboyant, extroverted characters to reflect off him. BR gets criticized for being "about" Catwoman and Penguin, when it's really about Batman's issues with duality, revenge, his mommy/daddy complex, etc. All Catwoman and Penguin are are reflections of these traits, amplified.
Plus, Robin is a very important part of Batman's development as a character. Without him, or any of these supporting characters, he's a very static character. HE, generally, is the absolute - I am Batman forever, it's something I have to do, I am isolated in my quest, yadda yadda. That's fine, but it's not going to keep an audience's interest for 3+ movies. Robin helps his growth, it's an outlet for him to deal with issues as a character that would otherwise never arise. It's good storytelling. Even Schumacher knew this; while he stumbled in many areas, particularly starting Robin off so old so that the father/son relationship became a brothers relationship, he knew that there were really rich avenues to take with the character. That doesn't mean it has to grow into the extended Bat-Family, but it's something for Bruce to deal with, which makes his character more interesting.