A granny type character could have worked, I could see the Doctor as a mama bear protecting her companions or a fairy godmother whisking them off on adventures. Miriam Margolyes or Angela Lansbury would've been great at that. Or a sort of icy schoolmarm or headmistress type, like Maggie Smith as Miss Jean Brodie or McGonagall, and like William Hartnell's Doctor. And that's just sticking to very basic clichéd female authority figure stereotypes, a good writer could've done so much with those as a starting point or done something different and interesting while sticking with the Doctor's character. Missy was a great version of the Master that brought something new to the role but was still the Master. 13 wasn't like the Doctor at all or even an interesting character.