This also brings to mind the actually ingenius "The Late Philip J. Fry" episode from Futurama. Except there, at least Fry, Bender and the Professor remembered what happened as they were the only ones who actually traveled through time.
This idea seems, as mentioned, very similar to the Doctor Who episode and even then not fully formed. Who are the people in this story? Why should we care about them? What's the point of it all beyond the big boom gee whiz battle scenes and 'splosions?
How do you plan to show these seminal moments from history? Are you going to recreate all of them with actors and sets and visual effects, or just ape stock footage off youtube?
It would be much more interesting (if you're adamant about having this particular direction being the thrust of your story) if there's a voice (or voices) among the characters legitimately asking if humanity deserves to be saved/rebooted. The ethical dilemma inherent in that conversation alone would be, if well written, a thousand times more interesting (and in line with the kinds of stories Star Trek has traditionally told) than another space battle.