Barbara's smart, compassionate, and brave. She has a damn good crack at saving the Aztecs, pulling off the role of divine avatar with conviction and an awesome headdress. Later on, she drives a lorry at a bunch of Daleks and doesn't flinch.

The Doctor may be right about her not being able to change history in "The Aztecs", but she's never afraid to call him on his bullshit, and she changes him as much, if not more, than he changes her. If it wasn't for Barbara (and Ian, who she has a lovely relationship with), the Doctor wouldn't care about humanity or Earth. Which would be a pity, all things considered - it'd be a very short show, for one!