Re: 8 years of no Batman or Bruce Wayne, and NO ONE could pick up the trend?
I still think that even with this interpretation of TDKR, TDK is essential to Bruce's arc. The irony of Bruce's longing for the cowl in TDKR is that in TDK he was hellbent on escaping the mantle of the Batman. And, in a way, Dent was still able to play the role of Gotham's hero indirectly via the Dent Act. This is what Bruce wanted at the beginning of TDK: a hero with a face so that he could move on and build a life with Rachel. The Dent Act wouldn't have happened without Dent's actions against the mob and the Joker in TDK. So TDK is still integral to the trilogy's story.
I respect your opinion about maintaining the Santa Priscan origin. I don't see any contradiction in Bruce's speech and the copybats in TDK. The copybats weren't doing anything heroic at all. They were homebodies who thought they could put down a dangerous drug dealer. In contrast, Blake was a trained officer with a working knowledge of the Law. That's not to say the fakebats couldn't be heroes. If you'll recall, Bruce referenced Gordon comforting him when he made his "hero can be anyone" speech. Anyone can be a hero, but not everyone can be the Batman. That's what I got from the speech and flashback to Gordon with young Bruce.
"Never call him that!" Spittle sprayed from Theon's lips. "Ramsay Bolton, not Ramsay Snow, never Snow, never, you have to remember his name, or he will hurt you."
"He is welcome to try. Whatever name he goes by."