I’ve said in other threads here how much I dislike shipping so, again, that’s a plus to me.
Barbara is so much more than cut from placid cloth too. And are you including the First Doctor in that analogy because, if so, that seems hugely wide of the mark.
The show also wasn’t conceived to have a format which included the sort of stories you would have occasionally liked but it is there. The Romans is a prime example of what you like and has more of it than The Two Doctors I would argue.