Some discussion over Pandora, the Mysterious Woman in the new DC Universe, posits her as a hero trying to get a broken timeline to work, and someone mentioned the Eleventh Doctor and The Crack as a comparison point.
And my first thought was I’d pick up that comic.
And my second was that this is indeed what someone like the Doctor would look like from the outside, in an ongoing series about a different group of non-time-travelling characters.
Of course, having a boy in a fez run out of a police box and stop the world exploding at the last minute would undercut the importance of the PCs’ actions, but Mysterious People observing and influencing significant events could be woven into games more slyly.
Hmm. I shall expound further on TWH.
Example: The Walker
A group of investigators looking into a disappearance notice someone watching them, who leaves if they approach - and vanishes when he rounds a corner if they give chase. And then when they get stuck, someone slips a clue in their letterbox...