Sirius is allegedly a father figure, but he's never given Harry any solid advice or tangible help.

*ponders*
Maybe...maybe he's meant to be a contrast to another "father figure" in Harry's life, someone who has always been there for him even if he doesn't realize it. *cough*Snape*cough*
J.K. did say that part of the reason Sirius had to die was so that another character could get closer to Harry...