Well, I think the idea is that any kind of “Time War” would be precisely to change the future because the assumption is that there are many alternate or parallel timelines. JJ Trek uses this idea (of multiple timelines), so it definitely holds sway in the fictional world of Star Trek.The very idea of a "Temporal Cold War" is ludicrous, because you would already know the winner before it even started.
For example, we know that no future time traveling faction traveled back in time and successfully killed Hitler in infancy.
You can interfere in history all you want, but it will inevitably result in the history we have experienced, and the future we will experience.
As for your example of Hitler; he is a real historical figure, with a real biography as apposed to a fictional character like say Colonel Green, for whom we could make up any thing we want. But on the other hand, there’s nothing stopping a writer from creating a fictional alternate timeline wherein Hitler was killed in infancy.
It all boils down to whether you subscribe to the alternate or parallel timelines hypothesis, or not.
In the real world we don’t know for sure, but in Star trek we “know” that it is so.
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