Oddly enough.. I was thinking along the lines of Jennifer Saunders, Joanna Lumley (remember Saphire & Steel?)
Or Jessica Hynes? Though I feel Saunders & Lumley too well known for Abb Fab.
Jody Whittaker looks to have all these qualities.. So a great choice.
I was reading an article this morning which made the point that it's quite a commitment to take on the role - you're filming in Wales for much of the year and it's very difficult to fit in other commitments around it. I suspect that both Saunders and Lumley have too much going on in their lives to take it on. Also, without being discourteous, Joanna Lumley has probably reached an age when she wants to take things a little more easily, and just make the occasional travel documentary. If memory serves, Jessica Hynes played Joan Redfern, a character with whom the Doctor fell in love during the David Tennant era (he was stuck in 1913, living as a normal person, for reasons that now escape me), so it would have been a bit self-referential, even for Doctor Who
.
There was a lot of speculation that Phoebe Waller-Bridge was going to be offered the part but I suspect she, also, is far too busy on things like Star Wars films and writing stuff of her own, to be able to spend most of her time in Wales for the next few years. A pity, because she would have been brilliant, but you can't have everything.