I think Batman needs Robin because without Robin Batman is basically heading straight for psychosville. Yes, Robin does have a calming effect on him, but that's not necessarily a bad thing. Also, in terms of narrative thread, the existence of a Robin allows for Batman to be a father, but a better father than his own (remember the speech Ra's Al Ghul gave him in the first movie about his father being weak and pathetic. Batman wouldn't be weak and pathetic with Robin around.)
Also, I think if you love a hero who is crazy and kinda sadistic, you might have a problem with the sort of people you're worshipping. It's like Rorsarch's fanbase. Alan Moore created him as the worst superhero ever, and was appalled when people said he might have the right idea. To idealise the traits which make the heroes closer to the enemies they fight is missing the point of the hero itself.
Robin does not make Batman family friendly either, if you want evidence of that just read 'Dark Victory' wherein Robin's inclusion actually serves to make the story darker, because now the ethics of Batman taking in a young boy are called in question, and Robin's backstory (or at least, Dick Grayson's backstory) is just as tragic and pointless as Batman's own. It's one of the reasons Dick Grayson was portrayed the way he was, because he needed that symmetry with his mentor.
Furthermore, Given that the first two movies have basically collected and reinterpreted Batman: Year One and Batman: The Long Halloween, if they wanted to remain true to this continuity, the next comic book is Batman: Dark Victory, and the introduction of Robin. Also from this movie's continuity, don't you think the choice of introducing a child character right after the love interest would have a great significance? My one love is dead, my parents are dead, basically, if Batman didn't latch on to any family figures, I would discount him as no longer being a hero worthy of my respect, rather than losing respect if he were to acquire a ward.
Besides, I think Tim Drake is the cooler Robin, but that would just be silly.