The argument that something is “logically incoherent” has been used to justify many a false conclusion about the observed universe, don’t do that.
Your other argument against time travel is better, but not airtight: it violates not the conservation of energy but the dominant energy condition in general relativity, Basically, for something to disappear, all of its mass has to vanish somewhere and no faster than with the speed of light. So maybe you get turned into a neutrino stream and or something. A better reason for why time travel (but not timeline forking) is incompatible with General Relativity is the uniqueness of the metric. But this is becoming a discussion of a real science, not philosophy.
Only commenting on one point here.
The argument that something is “logically incoherent” has been used to justify many a false conclusion about the observed universe, don’t do that.
Your other argument against time travel is better, but not airtight: it violates not the conservation of energy but the dominant energy condition in general relativity, Basically, for something to disappear, all of its mass has to vanish somewhere and no faster than with the speed of light. So maybe you get turned into a neutrino stream and or something. A better reason for why time travel (but not timeline forking) is incompatible with General Relativity is the uniqueness of the metric. But this is becoming a discussion of a real science, not philosophy.
If you were to ban every mode of argument that has ever been used to justify a false conclusion then it would be impossible to argue for anything.
Heaven forfend! ;-)