The way I see it, PoA is not the time for compassionate Sirius. GoF and OotP are for that. He's meant to be a mass murderer, he's been locked up wrongly for twelve years, of course he's going to be a bit batty and rightfully cheesed off. He simply could not go from murderer, to insane, to angry to compassionate all in one book or film. It would make no sense and seem rushed. GoF is the main place for the Sirius/Harry relationship to build. Realistically and cinematically it would've looked bad if a character had changed too drastically in the course of one film which is why we only saw one glimpse of compassion so that by the end, we know he's good.