"We don't see time travelers. This means either time travel is impossible, or humanity doesn't survive.
Evidence of the theoretical plausibility of time travel is therefore strong evidence that we will be extinct in the nearer term future."
Except for the fact that those aren't the only two possibilities. There could in fact be time travelers, but they remain unseen (either purposefully or not). And this would be a possibility for a long list of reasons .
Also, don't lose the forest for the trees if you know what I mean.