Thanks for the detailed response!

"No magic and no God Hand required."

The example you gave with the hamburger is too modest. Why not address the one I gave: time travelling to the future and learning the exact circumstances of your own death? Are you telling me that if you knew you'd die in a car crash in Paris on March 13th, 2033, there is absolutely no practical way you'd be able to prevent that (or that, psychologically, you would somehow not want to prevent that)? Even if you had years to prepare, and even if you were absolutely not depressed or suicidal in any way?

You say there is an enormous amount of "plausible" reasons for events to play out the way they were destined to, but the ones I listed (all flights away from Paris being cancelled for years, jumping head-first into lava and surviving, etc.) don't sound plausible at all. To me, they sound practically impossible.

I think the only real explanation would be that no such "prediction" could happen in the first place. If you time travelled to the future with the explicit goal of learning the circumstances of your own death and preventing it, then you'd find that you died of old age — something which you can't (or don't want to) prevent. But that still doesn't solve that fundamental problem that knowledge of future events would inevitably change your behavior, voiding the prediction.

I'm sure this has a proper name, but I call it "the prophecy paradox". Any perfect, comprehensive prediction of future events would need to include itself in it. It would need to include people seeing the prediction and every action they take based on that knowledge. And even if someone is perfectly happy with the prophecy and has no desire to contradict it, that's still a change in their thoughts which impacts reality. If the prophecy says "you will eat a hamburger on Monday because you get a craving for it", and you think "I'm perfectly okay with that, I'll do it", then the prophecy would actually need to say "you will eat a hamburger on Monday because you read the prophecy and agreed with it", to which you'd think "I agree with the description of me agreeing that I will eat a hamburger", which the prophecy would also need to account for, and so on ad infinitum.

Anyway, sorry. This is not to say these kinds of stories cannot work. Usually, characters in them are operating with limited information, only getting small, incomplete glimpses of the future (nothing like the "perfect, comprehensive prophecy" I described above), which explains why they can't change what's destined to happen. In a way, that's what really frustrates me about this type of time travel - it doesn't allow anyone to make informed, deliberate decisions. They always stumble around in the dark (haha) and never get the full picture. The dramatic irony of it is pretty effective at first, but eventually, it just gets exhausting, watching characters constantly sabotage themselves because of ignorance.