Re: this is a little tl;dr, but...
This comment really made me think about how I think the Batman/Robin dynamic is unique. I mean, there are noir elements, but noir is usually about a man alone, outside society. (Though there can be kids in a noir if they're also outside that society etc.) But Batman isn't that and really never was--he's a respected part of society and has a home in Gotham City, which thinks of him as their own protector. That he would secretly be taking in kids who've been let down, abandoned or separated from their parents by crime makes sense to me as I understand the character, especially given that this is a superhero comic. He's not alone because he really has a very straightforward idea of how the world should work: people should take care of other people who are weaker etc. So he gravitates to other people who do that.