One of the biggest problems with TimeTravel is the potential for creation of impossible TimeTravelParadoxes?. But there are many other potential TimeTravelProblems such as the GrandfatherParadox, but far less dramatic examples could be equally ruinous.
For example, assuming that TimeTravel could be limited to very small amounts of information, it is possible that someone could use it maliciously to send misleading information into the past to manipulate the timeline or even destroy the HumanRace.
Our willingness therefore to receive information from the future would have to be something in itself limited to RandomMeaninglessness?, such as some type of Quantum information like a series of QuBits.
Okay, let's face it. The biggest problems are TimeTravelParadoxes?. It would seem that they preclude all conclusions.
Paradoxes make for fun thought experiments, but are logically and physically impossible. Chances are that TimeTravel is possible (at least, we have no reason to believe it impossible due to the SpaceTime relationship), but it is our intuition of cause and effect that is problematic. If quantum physics and the matter-wave relationship holds, it is also quite possible that time travel to the past will actually involve travel to alternative histories and that we beings of matter can only experience a small fraction of the spatial-temporal universe that follows many paths, strengthening some and destroying others. (If so, other versions of us are experiencing the small fraction of the other possibilities in which we were born and somehow remain alive.) If you go into the past to kill your Grandfather, perhaps you'll succeed in a senseless murder then end up in prison (without a legal identity) in the alternative history, while friends and family from your original path will simply wonder where (and when!) you went.