How do you figure the fight against the Black King is the common diverging point for all the timelines those doomed Aradiabots are coming from? There could be any number of things that make the game unwinnable. Dave had to travel back in time to stop John from dying on day one, and the trolls were playing a harder game for more time. What I think is happening that every time Aradia fixes an error in the timeline, she skips to the end to fight the Black King to remove herself from the game. She's doomed anyway. Although I guess this means that she did attack Vriska: that was not a doomed timeline, that was a successful timeline, made such in part by Aradia attacking Vriska.
It would have to be the common diverging point. By
necessity.
If an error in the timeline occurs before the Black King fight, Aradia traveling to the future to the Black King fight will have
no effect on the outcome of the successful timeline, because the timeline is already doomed at that point.
If an error in the timeline occurs during or after the Black King fight, Aradia can travel to the past to the Black King fight, and she will affect the outcome of the successful timeline, because the timeline is not doomed at that point.
When errors occur that make a timeline doomed is important, not just that the timeline is doomed.
I guess she's not using this power to save herself because, well, being dead amplified her psychic powers, right?
It apparently had to be this way and there was no other way it could have happened. Obviously proven wrong by attempting to retroactively fix timelines, but on a larger scale it can still be argued that there is no other way it could have gone. I.E., it was still predetermined that all of those timelines would be doomed and all those Aradias would go back in time to fix it.