I really like the part of removing paradoxes from the equation. It's one of the most irritating parts of any time travel story. The alternative is, usually, the Multiverse, where every time you travel in time generates a whole new universe (or you simply get transferred to another
already existing universe out of an infinite number).
The question is that it makes the whole travel quite pointless, except to you. A person that died is still dead in your original Universe. Only you can experience the change, because to all the others things are just what they always were.
That ghost hypothesis also solves another question: What happens to the atoms that occupy the space where the time traveller materializes? A big ball of thermonuclear fire is one possible answer...
The last part, realizing "We are all ghosts now" takes us, I believe, carries us to a curious paradox: The present, on one hand, doesn't exists, always slipping into the future. On the other hand there's only the present. The past is gone, the future doesn't exists yet. I'm sure some philosopher already dived into those deep questions, but right know I'm to tired to check...
Anyway, we may be all ghosts now, but that's all the reality we have.
Last thought: Almost all time travel stories* chose to keep the travelers anchored at their spacial reference, which is very practical in terms of storytelling, but really not guaranteed. Since earth, the sun and the whole galaxy are moving (at mindblowing speeds) a short time jump would put our traveller very far away. I remeber someone refering that when that asteroid hit earth, killing most dinossaurs, our planet was almost on the other side of the Milky Way...
* there was a story, whose name and author I don't recall, that uses the time-space displacement. I remember they have a mouse on a cage and they use their time travelling device on it for less than a second, and the animal show up outside the cage, and a bit
over the table...