... some President or intelligence chief
I doubt that "some President" would be wielding this power. It is much more likely that he would be the subject of the power. First off, the agency would be loathe to be controlled by an external political agent. Secondly, it seems like it would be more useful to have a disposable puppet in charge rather than put one of their own in such a highly visible and yet temporary position. After all, their normal MO is to work in the shadows.