Oddly enough, they want to specifically use the word "power" because of its existing reputation, i.e. its connotations with acts of non-consensual control. They may say something like "real power does not stem from violence, real power comes from a group and does not exist without group coherence." However, the only reason they're focusing on the word "power" is because they know what it implies and are using its reputation as a concept in order to lend credibility to their own ideas, which themselves usually contradict the agreed-upon meaning of the "power".
To be clear, this may not strictly apply to Hannah Arendt, but I see other people playing with the word "power" so frequently that I thought it was relevant to mention.