Pertwee yes, because he was stuck and trying to leave. But as for the rest of the Classic series? Not really an arc.
Whitaker has as much “feel” as any other Doctor of the Classic series. In the Classic series, the Doctor rarely had anything going on internally. He basically was all external. Which was very much TV at that time.
Pertwee was also the Doctor brought down by arrogance and had the Buddhist themes underlying his final stuff (the crystal from metebelis was seeded long before...yes, it’s all a bit made up as gone along, but stuff was seeded in case they needed it later) Baker...nothing at the beginning beyond the Toulouse Lautrec bohemian, but later it gets a bit bound up in Time Lord politics and the Guardians...and the overall arc of dealing with reborn master that ties up with that. Davison is the ‘feckless’ Doctor, Who is actually about innocence and naivety (not to mention the hidden face beneath, highlighted by his ‘idiot’ nature in Kinda.) and is ultimately about sacrifice. The sixth had the planned arc that we see again with Capaldi...he’s nuts, and very alien, steps over a corpse, cries at a butterfly. The Dalek arc that arguably inspires the Time War is in this time, carrying through fourth fifth and sixth, and the Doctor as angry agent of the Time Lords is more pronounced in the sixths run...not to mention his trial. The Seventh certainly has an arc, but it only really solidifies once Cartmel gets his feet under the table. It’s best summed up as Times Champion, and Ace certainly has a massive arc, all of which seeds growth in the later novels. Now, the TV series cant fully address the novels, but nor can it ignore them...and it’s here that the simpler characterisation really sheds its chrysalis. The new Doctor feels like an attempt to put the genie back in its bottle, and I am not sure it’s working. The show has fifty years of history, the character has a couple of thousand, pretending it’s not there, that almost nothing is, doesn’t entirely work anymore.