My headcanon re Anna's fall is that sometime around summer 1978 Michael and Uriel started treating her differently, and neither of them might ever have admitted why but the rest of the angels picked up on something being wrong and they also started treating her differently, and after a few years of being the sibling nobody plays with and the soldier who gets all the shit jobs and the commander everybody obeys in letter but not in spirit, she attempted suicide. I'm not sure whether she thought ripping out her grace would kill her on the spot (and if so it didn't exactly go as planned) or if she meant to be born human, but either way she would have lived human for a while and died human and that would have been the end of it. And of course while she was living human she got to be real sympathetic towards humans (or more sympathetic, depending on whether she intended to become human), which is what sent her back to spring 1978 in the first place. Just like with 4x03 and 6xWestern, 5x13 is a closed time loop that couldn't have happened if it hadn't already happened.