That is just because you are not thinking carefully enough about the consequences of the rules you are making up. Start really thinking about it and you will pretty surely discover a lot of contradictions, paradoxes and so on.

Not really. There are three basic ideas with time travel. Either time is independent so if I go back a second a pick up my wallet I can come back and have two wallets ( aka multidimensional time).

Consistent where doing that only works because a future time traveler took my wallet so I just end up with one (Self consistent aka Harry Potter time travel).

And one way which basically means if I go back there are now two of me and I have to go forward the slow way. Which is separated from the first example by erasing the future when you travel back.

Paradoxes are only an issue in the second example.

Your first and third scenario seem not to honor conservation laws, one can probably build some nasty consequences out of that. Or what happens to the matter occupying the space you are about to appear in, where does it go? In the third scenario it can not simply switch places with the matter from the future because that would kill the asymmetry of that scenario and provide a way to send stuff to the future. I was not simply talking about you killing your younger self. To have any real merits one has to analyze a time traveling scenario with the same mathematical rigor as our normal physical theories. But I never thought much about about time travel because it is such an hypothetical idea and therefore my example a probably pretty bad but I hope you get the idea of what I am aiming at.

Conservation laws are man made, if the underlying universe does not follow them then so be it.

As to other interactions their are a great many possibles but they don't mean much. For example restricting things so only light can move though time does not change the underlying options in terms of information and paradoxes.

PS: Mathematical rigor is again a human idea, our universe could be absolutely random and we would have no way of knowing. At best we can say that seems unlikely.

Well, we can also just say the same things about paradoxes of all types. Partially the point of science-fiction (and science/philosophy) is that our thought experiments have parameters consistent with our current knowledge of reality if no other restrictions are specified.

I've been planning on writing a novel based on that for about twenty years now. I've even started it a couple of times. I certainly hope someone "steals" our idea and runs with it.

Michael Crichton did it.

It's how the time machine worked in Timeline.

If I remember correctly, the company sending people back through time (really to a parallel universe) didn't even know how/why the receiving machines were appearing.

It also happened on Sliders, they visited worlds that were ahead or behind Earth Prime.

Not exactly the same idea, but Steins;Gate deals with time travel as travel between parallel universes in a similar way.