Does Perfikot covet power? That is likely not the case, at least she doesn't believe she desires power.
But for Perfikot, being without power simply isn't an option.
After all, what she wants to achieve cannot be accomplished without power.
When she was without power, whatever she tried to do met with opposition from various sides, even when she wanted to warn the authorities of the impending apocalypse, no one paid heed, and she was even regarded as a lunatic.
However, once she possessed power, no matter what she intended to do, others had to take her seriously.
Although Perfikot doesn't covet power, if she wishes to prevent her efforts from being wasted and avoid seeing everything she worked for destroyed, she must have power.
She doesn't trust the nobles of Langton, in her eyes they're nothing more than a swarm of pests.