Let us assume that we do not yet have a time machine, not because time travel is not possible at all, but because it is not possible in physical terms.
In this paradigm, the hypothetical temporal traveler would be sent into the past or future by a time machine that would be anchored to “their” present.
And since we have already established that a time machine, should it exist, would be used infinitely, the corollary is that any traveler could not be present in the non-native timeline in their physical form.
After all, we occasionally hear from a madman who claims to have come from the past or from the future; we do not hear from hundreds of them. And the few we hear from are always quite ignorant of historical facts, and incapable of getting right the most pedestrian of predictions.
Therefore, if time travellers exist, they will be more like observers; they can see other timelines, but not interact in them. Or if they do interact, it would be in a way that would be indistinguishable to what we call “the supernatural”; for us, events occurring from their actions would look like an inexplicable phenomenon.
But here we return to the problem of infinite reuse; sure, whenever it would hypothetically be invented, a time machine could be considered a dangerous and difficult instrument to produce. But let’s not forget how little time it took for us to go from a world where there only existed two atomic bombs, in the possession of a single country, to thousands of them scattered all over the world.
Technology multiplies exponentially. If it were possible to send people to the past, and if the manifestation of it their actions would equate to what we call the “supernatural”… Every house would be haunted.