According to a new joint interview with writers Steven Moffat and Russell T Davies, thinking of the Doctor as segmented incarnations isn't really how they approach writing the character at all. In fact, instead of the great differences between incarnations, (that fans love) to debate, Moffat and Davies seem to indicate that they never aim to write the Doctor particularly differently and that thinking of the character as a constant is the paradoxical secret to making each version feel authentic.
The Late Night host humorously mentioned, "I'm going to read some real jokes, really submitted by my writers. Some are dumb, some are offensive, some are just insane. Most importantly, my writers don't know we're doing this, and because they don't watch the show, they'll never know." This highlights the spontaneous and irreverent nature of late-night comedy, showcasing a blend of humor that includes the absurd and the outrageous.