Episode III too focused on Anakin's story
I watched Star Wars all over again and realise that Episode III's focus on Anakin's story (as admitted by George Lucas himself) is actually not doing justice to the other elements of the saga, and on the contrary does not contribute to its holistic continuity.
The Invisible Seeds of Rebellion
The original trilogy has an essential backdrop of the Rebel Alliance fighting against the Empire, with the story of Luke finding his destiny in redeeming his father and becoming a Jedi. The decision to remove Padme and the Rebel Alliance series from Episode III gives a loophole in the continuity of the saga, as it would be important to actually at least established that there were significant opposition to Palpatine's rule, they who would later rebel against the Empire. Episode IV would then makes more sense with its beginning reflecting this situation.
Yoda's Exile
Even the last shot of Yoda landing on Dagobah was removed for it would disrupt the focus on the thread of the children, as said by Lucas.
Backdrop Established even with Anakin's Story in EP I, II
Even if the prequel trilogy was to be the story of Anakin and the original trilogy that of Luke's, there is no reason to compromise other essentials of the saga in favour of Anakin's turn.
For one, Episode I does elaborate on the backdrop of the trade federation's aggression but still essentially include the re-emergence of the Sith and the founding of the alleged Chosen One. Episode II too details the inner workings of the Sith on the Republic's fate thru the separatist movement and still include Anakin's love and lost of his mother.
Padme and the Droids Compromised for Vader
Episode III while it explains the fall of the Republic and including Anakin's turn, becomes too exclusive in the latter, not only compromises the continuity of the saga as a whole by excluding the seeds of rebellion, it also does not do justice to Padme's character by cutting off her continuity. In the previous Episodes we see her as a respectable diplomat of influence in the Republic, but Episode III only focuses her as a wife and childbearer of the children. The supposed dark theme also virtually removed C3PO and R2D2 from the film, they who were so significantly portrayed in the OT.
Thus even if Episode III is supposed to focus on Anakin's turn to become the infamous Vader, the virtue of the original trilogy itself proves that the character of Vader was but one of the many essentials of the entire saga.