I think I finally see where you're coming from, El. But I think it's because you misinterpet what Batman and Robin is about. In retcon Batman didn't really adopt Dick, he was a material witness in the murder of his parents and Bruce just provided him a safe and temporary place to live out of guilt and empathy. We agree on one thing, Batman never wanted Robin. Bruce isn't out to be Dick's dad or his best friend, just his mentor.
While in the care of Bruce it became obvious that Dick was out for vengance. He wanted justice, just like Bruce did, but Dick was willing to run off into the night to find that justice. Training, or no training; Bruce or no Bruce. He was alot more wild and reckless than Bruce was at that age. Of course Bruce saw the vengance that raged inside the boy and he sympathized with it, how could he not? Batman gave him a path, a focus for that potentially destructive rage inside Dick. He tutored him, trained him, and when BATMAN thought Dick was ready, he became Robin.
Let's get one thing really clear. Bruce Wayne is not a responsible person. If he was, he would have become a cop or homocide detective. He wouldn't dress like a bat and maim criminals every night. He wouldn't cause untold property damage in Gotham city. Bruce is unhinged, and he is a living id. Bruce Wayne would have no issue with allowing Robin to fight crime. Does that make it right? No. But Bruce allows it. I think you're starting to forget Batman isn't quite sane.
Also, here's a story about how well the adoption service in America works. A woman I saw on the Steve Wilkos Show adopted over 41 children, one of whom was wrongfully imprisoned for child molestation for 10 years. The woman proved herself to be irresponsible numerous times, but that state allowed her to adopt a child 41 times! Knowing this, how unrealistic would it be for a billionaire to be allowed to do it once? And like I said, Bruce isn't out to be Dick's dad. It takes years for him to officially adopt him. Bruce is merely a benefactor to Dick in the public's eye. He doesn't want to adopt every orphan, he just wants to help Dick. They are two men on the same mission, and Batman is making sure Robin does the mission right.
I think your issue, El, is that you're assuming certain factors about Robin and Bruce Wayne instead of researching a little. You're posing yourself as the authority on the matter. " The character is uneccessary and goes against what Batman is and is there for." That's what you said, right? But who are you to presume that when, in fact, that has been part of the character for so long? You, in a bit of arrogance I think, are saying that dozens of creators over decades of history are wrong.
Batman isn't Frank Castle. He isn't a heartless machine of vengence. Is he dark? Yeah. Withdrawn? Yeah. But that isn't his limits to that. He's still a man that needs friends and partners in his efforts. There's a big part of him that is sympathetic and passionate about the plight of others. It is that part of Batman that makes him a righteous tool of justice instead of a maniac hell-bent on revenge. It is that part of him that feels for the orphan Richard Grayson. It is that part of him that can't deny Dick the very thing he has dedicated his entire life to. It's the core of Batman. He's a man, human and flawed. Alone, sad, angry, joyous, excited, right, wrong, sympathetic, vengeful, and all things in between. The reason we all love Batman is because he is human underneath it all. The origin of Robin is one of the greatest displays of that humanity in the Batman legend, and that is why so many want to see it realized correctly.