I think my favorite argument against the likelihood of time travel machines is the physical impossibility of backward time travel.
It's not proven to be physically impossible, and the possibility even comes directly out of (current understandings of) space-time equations. As was said in the intervening interval between our two posts,
most theories involve preparing your time-machine(/gateway) so that until it exists you can't have had someone coming from the future who will have eventually had the opportunity to make their future travel into the past that is your now.
Which is not to say that there aren't already such twists, waiting (fated!) to be used - and therefore
have been used, already to exit in your past. Maybe you having done so.
And the theories of how they then work with paradoxen tend (in the absence of experimental evidence) to support the self-sustaining causality loop (a billiard ball heading towards a time-travel billiard-pocket that would eject the spheroid out to interfere with its past self and cause it to miss (which would mean it did not get opportunity to deflect itself) is an unsupportable energy-balance, whereas the ball that
only goes into the pocket because of a collision by its future self (an event that must already have happened) is fine.
Self-bootstrapping events are fine (see also
All You Zombies) although not in isolation (a ball that appears from the future to become the ball that goes back into the past) has various problems with personal stability given the non-zero chance of (among other things) proton decay that must occur over each iteration, making for transfinite changes each time round, which is
every time around.
Which is not to say that it might not be different in reality (if we ever identify such a thing as 'reality'), but if anybody's come back from the future to give us the proof that irrepairably altering your own timeline is possible but results in you fading away (while performing rock music) they
may have only been taken seriously by a scriptwriter, not any scientist (not otherwise invested in the project).