@OnLeatherWings
My head canon has always been....
There are definitely adventures between Begins and TDK. A whole year passes. Even Gotham Knight explored some other rogues popping up in that in between period, even if it's not A-level canon.
And as far as the 8 year gap, I think there is some wiggle room there too. For one, he has a whole new Batcave and we know Wayne Manor was still under construction in TDK. Alfred says, "you haven't been down here in a long time"-- which in my eyes, always confirmed the fact that he's obviously been down there and used it before. There is an unclear amount of time between the night of Dent's death and the passing of the Dent Act. Then we have "last confirmed sighting". Which of course alludes to the possibilities of some 'unconfirmed' sightings, Batman kind of receding back into a bit of an urban legend. The way I saw it, Batman could've been super-stealthily active for some period between TDK and Rises. Maybe no 'major' events happen in that period, but I think there could've been small scale stories where he's staying vigilant as the city recovers from the events of TDK, eventually leading to the passing of the Dent Act/IE the final nail in the coffin for organized crime in Gotham-- which was always his mission statement. As far as the knee injury, I always saw it that it would've deteriorated over time left untreated. I didn't think of it like he'd been walking with a cane for the entire 8 years.
Now I get it, it's not the sprawling Bat-universe full of 'freaks' a lot of fans had hoped it would be building to after BB/TDK, but I do think the movie offers enough little nuggets to imagine what might've exactly happened between films. I don't think it's exactly clear cut, and it's something I actually thought a lot about after TDKR came out. But I definitely landed on the side of, it's left open enough to imagine certain possibilities.
Personally, I think sometimes fans get overly caught up on the idea of how much time he's clocked in the cape and cowl and are weighing it against 80 years of history and the fact that Batman is a constant. I think if you take a step back, and just accept it for what it is- a uniquely finite cinematic interpretation of the character, I find it's easier to accept.
I think it's worth revisiting the films, and just appreciating what they have to offer. Even if they don't represent your personal Batman, which is fine-- IMO it's still one great big Batman story where it's greater than the sum of its parts. It's the only beginning to end version of the story that exists, really. I think what you may lose in head canon and a world that you can tell infinite stories in-- you gain (at least IMO) the satisfaction and closure of having gotten to witness an entire arc that takes us from Bruce drifting across the globe, training with the League of Shadows, to putting together the idea and methods for his mission, his first night in Gotham, encounters with some of his most important rogues and echoes from some of the most iconic comic runs, all the way through the end of his mission. And the 8 year gap allows us to see how his legend grows in his absence- IE. we see how the orphans still believe in the Bat, despite him 'becoming the villain'. I think stuff like that makes it a richer story.