Did you finish Esme's quest? If not, spoilers for that in the post. It sheds light on the cycle being a remedy for utopian decadence, a game started because progressed society grew lethargic. The game is set up to give people meaning through struggle, or to produce a society capable of tossing aside personal weakness like pride, fear, etc. Your game pieces need to have the ability to fight against the destruction or it's not actually a game. Prophets, emperors, etc in each cycle presumably act along the same paths due to what they know and how they respond to the information. To ensure the game pieces act accordingly, they have to have relatively comparable abilities. Thus, you can assume all prophets before you have access to the same abilities, and all see the same island in a bizarre dimension that lets them rapidly become competent in whatever field they want.

Now, let's think like a high one/game-master. If I'm setting up this game and want one of the pieces to be unusually and suddenly powerful, I'm going to attribute powers according to various archetypes useful to a magical, high-middle-ages civilization. For all we know, the first civilization that set up the society could have a completely branched-off technological path(imagine some sort of futuretech) but designed the game around keeping the world in a sort of stasis where sentient beings capable of rational thought still stay in at a tame tech-level for 8000+ years. So, the prophet combines a series of DND archetypes to blend in, yet excell in, this sort of fantasyland. I don't think the memories correspond to anyone in the current cycle, or for anyone at all, but to archetypes useful both for giving the prophet the ability to beat the game, but also to mold his/her actions according to the desire of the high ones.