Spot on!
I would disagree about Dick being the only ''successful'' Robin. Tim was a pretty successful Robin too. But I agree that he didn't have to be Robin and was leading a pretty normal life. So yeah, seen in that vein - Dick could have gone down a dark path after his parent's were killed so becoming Robin was a net positive for him. Jason would also have gone down a dark path, and after being killed and resurrected, he's still on a dark path, albeit one that's kinda doing some good so...I guess its 50/50. Tim was leading a normal life before he got involved in Batman's world as Robin and suffered some tragedies, so I'd say its not a net positive, but maybe not a net negative either. For Damian, being Robin is a net positive, but he's starting from a pretty bad place (and as I've said, I feel he's something different from the classic Robin concept). For Steph I guess its a net negative since she died, but she was a vigilante already so...
But yeah, I agree that Robin being Batman's sidekick is a bit of a pop-culture hangover now. Back in 1989, even though the comics had toned down his influence on the Batman mythos over time, most people still associated Robin closely with Batman thanks to the 60's show and the Superfriends cartoons - so excluding him from the Burton film was a big deal. Today, if Reeves or anyone else chose to include him in a live-action project with Batman, that would be the big deal!