In a world with time travel into the past, there's no causality. So, there's really nothing to be concerned about.

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Causality shakes hands with itself behind someone else's back, with two different peoples' hands.

That's kind of how time works.

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<-- (i.e., this, slightly scaled)

Since our world has causality, to me this implies one of two things about time-travel-to-the-past:

1. It's impossible.
2. Even though it's possible and therefore causality is broken, the world tries really hard to pretend otherwise.

Assuming option #2 leads to all sorts of brain twisties. The same sort that occurs when you are planning an RPG in which you introduce a vector through which the PCs can pass messages to their past selves. @_@;

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For me, a while back I settled paradoxical time travel like this:

1. If we assume that time travel into the past is possible;
2. And if we assume that such time travel can create conditions that would have catastrophic consequences at various points in the past;
3. Then time travel into the past is impossible, because the present still exists.

That is: at some point in the future -- perhaps in the distant future -- such time travel would be accomplished, and despite all attempts to regulate or control it or otherwise prevent a disaster, at some point in perhaps an even more distant future an accident or act of maliciousness would happen, and at that point or some later point it would happen either in our present or in our past, having catastrophic consequences in ways that we would perceive.

Since that hasn't happened, then it can't happen.

That leaves just two possibilities: either time travel (to the past, or the future) is impossible, or, if it were to happen, it can't possibly have catastrophic consequences.

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That makes sense, and probably is even necessary via the Anthropic Principle -- though depending on whether you subscribe to the weak or strong version thereof, it's hypothetically possible that time travel is inevitable in any sufficiently advanced civilization, and because of observer bias we're just in the one universe out of the brazillions and brazillions that managed to go its entire run without destroying itself.

(That having been said, your version is certainly more intuitively plausible.)

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If an advanced civilization destroys itself retroactively through time travel, is it still an advanced civilization?

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That would certainly explain the Fermi paradox!

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