Well, ofc there exist plot-holes. Time-travel aint even officially science. Scientists themselves have problems with time paradoxes, you can't expect an author to handle it 100% without any missteps. BUT , on the otherside it is an awesome way to foreshadow great things, cuz you know, they happened, just not yet. Even the almighty Steins-Gate had problems with it but in the end it worked and it became an awesome anime.
I, too, was against time-travel back when the hooded girl showed her face to Gerard and the theories began, but if you consider the possible scenarios that might follow you can't but get hyped up.