Definitely now he's a friend and comrade as well as a son, and in some ways always was, I agree--this is true with all of them since Bruce has no kids who aren't also Robin. Most good parent/child relationships eventually move into that, and for them it's far more so because they were always comrades in arms. I don't think Bruce took Dick in truly aware that he would be a father-he probably couldn't even conceive of such a thing, but for me that's what just makes it more real. He took Dick in on impulse, having watched him lose his parents at the same age Bruce lost his and in a similar way. There's more to their relationship than father and son, but given all their obsessions with family that aspect of it means a lot imo.
For me, also, the sliding age timeline is less important since nobody's ages make any sense when it comes to that. I've read plenty of stories where Bruce is an adult man taking care of a boy, so I can't think of any time Bruce seemed too young to be Dick's father. Those older stories because that's Dick's entire childhood. He grew up in the golden, silver and bronze age and that's still his canon.
That's also why I think the later stories make it a source of pain for Dick, because whatever Bruce wanted to tell himself he was, to Dick he was a father and more. Denying it to cover himself emotionally, or because he feared it was too much to ask, was hurtful. Not the legal adoption aspect because when Bruce originally said he just didn't think of it way back Dick could understand that, but any implication that he didn't accept Dick as a son. So I've got the old issues where Bruce seems to totally act like a proud father, then the modern stories where they talk about being father and son. They did, I believe, once even retcon the adoption and say that Dick was adopted right away, but I think the reason people ignored the retcon was that the whole "ward" thing was so well known, and people felt like it needed to be addressed.
Part of it too, I think, is culture creep. I think there's a real difference in what behavior was expected from a father in the past, so there might be different cues that people would recognize as Bruce being a dad or not. In Disney movie terms, it's more Bambi than Lion King.