Barristan is a knight looking for a ruler, a hero looking for a cause. I'm not sure where he is without one.

I'll concede Cersei point because I don't remember or didn't read those parts.

If you look at male-female relationships, Stannis needs Melissandre. Does Melissandre need Stannis? Arguably, but I think it's more accurate to say she's using him. This is, incidentally, illustrative of a very common theme in the real world that wars start out as political conflicts but become overrun by religious agendas.

As far as Arya, I think "need" is the wrong word. The men in Arya's life are devices to get her from point to point. At various points she needs them for instruction or survival but she's not tied to them. She's a central character and the dominant one in every relationship. This extends all the way to her family. She "needs" instruction, protection, a sword, a talisman, to get her to her next step. She's not running around the countryside going "OMG I need to find Jon Snow/Jaqen/The Hound" etc. and she's happy to leave them once their purpose is served.