Keeping in mind that, in many cultures, removing your shoes when entering a room is a sign of respect, you can say that podiatrists do have power of sorts. They also have the semi-biblical ability to help the lame walk, which adds to the power quotient.
The serious reality is that a podiatrist works to make people who are in pain or discomfort feel better. They take on the mighty responsibility of caring for the health of their community, which ends up being huge on the power scale. We wouldn’t suggest starting a life of crime fighting or taking on any rogue nations with your new sense of power, but it is power nonetheless.