Television is our safety, our constant. Much like reality and real relationships, we can't always count on it not to hurt us. Just like our own selves, these characters have flaws. No one lives a perfect life, not even a fictional television character, no matter which pair of rose-colored glasses you wear to watch.
There's nothing particularly wrong with employing the time-space continuum for the pure fun of the concept. Edge of Tomorrow makes good sport of it, but, given the mind-bending possibilities inherent in the genre, it seems almost a crime not delve for deeper meanings than just "craven coward becomes kick-ass action hero."