Of course it wouldn't be time travel. People who were especially good at predicting other people's life paths would just do so and punish accordingly, or something.
Edit: I accept your point that future consequences don't suffice to justify time-travelling punishment.
Here's an edited version of a puzzle from the book "Chuck Klosterman four" by Chuck Klosterman.
When should you punish someone for a crime they will commit in the future? Discuss.