But would the speed of changing focus on arm pairs offset the time to move hands to a different part of the controller?
It sounds like it's basically the same as having the normal human complement of body parts: it's very difficult to do two or more independent and complicated things at once. But switching is basically instantaneous, and practice, muscle memory, and combining the separate motions of different parts into single, combined motions can allow for quite complex multi-limbed actions or automatic background processes.
In the case of a video game, I imagine it's basically like using a controller normally with two hands. You don't have to think about switching from one thumb to the other, or from your thumb to your index finger to activate the trigger buttons. She just has extra fingers to handle the buttons. So better physical response times and easier button combination presses, but the overall complexity of her gameplay wouldn't change much. And she probably couldn't, say, control two characters at once with two controllers particularly well.