Speaking as an actor, I do like the opportunity of playing the same role under different direction. I speak from stage experience only, but it's fun to do a role in a play and then to do the role in the same play directed by someone else. It allows me as an actor to flex a bit as well as work with new talent.
Maybe we're spoiled by the NuWho history, but in classic Who several Doctors did go through different lead writers / producers and came out well for it. Tom Baker could arguably be the best example by his own longevity through several rounds of this, with both high and low points (and near legendary conflicts with lots of them) included. As it stands, I think the only real example in NuWho would be the episode of The Sarah Jane Adventures which had RTD writing the Eleventh Doctor, and you could clearly sense that he was just sticking to his mantra of writing "The Doctor" and letting the actor take it from there.
I would like to see Capaldi do a year with Chibnall, to see what one Doctor would fare without the tropes of a single writer. The latter would certainly work to avoid being a John Nathan Turner to a Tom Baker...
Mark