I also think the role of the assistant has changed since Steven Moffat started overseeing Doctor Who. Rose, Martha and Donna were chosen to travel with the Doctor because they showed in one way or another that they were smart and up to the challenge. Amy and Clara both come to the Doctor first and foremost as mysteries. Amy is the little girl who grew up with a rift in time in her bedroom wall, who doesn’t know why she doesn’t have parents. She spends many episodes being mystically both pregnant and not pregnant but doesn’t know a thing about it and all our information about it comes through the Doctor. What the fuck is that?
Some version of Clara dies on screen twice before she is taken on as the assistant, and it seems like the Doctor takes up with her to find out why. In both cases, the woman is not of interest for her character or her abilities, but for some fundamental mystery in her being. The mystery isn’t even a secret she’s keeping, something over which she has control- it’s something she does not know about, that the Doctor must puzzle out in his own mind. It’s not about her- it’s about what’s wrong with her. When Steven Moffat took over Doctor Who, women became a problem.