Damian has other issues than mere socio-economics (kinda like Cass and Helena), and thank god for Dick, but otherwise and except for Dick, it's all a little worrying. Babs is Oracle, but she got KillingJoke'd. Jason died, Steph died - leaving aside the incompetent/a bad seed/they deserved it angle - both deaths were supposed to be permanent. Bruce and Tim are okay.
I tend to think of it as something Jason retroactively created
I don't think entirely. He probably did, at least a little, but I doubt a kid fresh from the streets wouldn't have felt something in Bruce Wayne's world. Now, whether Bruce would have understood it, him, is another question. I guess it depends on how crazy you imagine him as being at the time. The more Batman#416-looking-for-a-replacement-Dick you see him, the more he's likely to have been blind to Jason's reactions and feelings. And that Red Hood!Jason would refuse to admit that Bruce might or at one point did understand him is a no brainer.
Jason's training was provided in part by Talia, giving him the names or putting him in touch with the same people who'd trained Bruce himself, so I'm inclined to let that one slide.
their personalities were designed Yup. It's convenient that of the three Robins created in times when verisimilitude or character psychology became much of an issue, the only one to receive that gift is the rich one.