Well, apart from the story you play out for your own CMDR of course, the life he/she lives in this galaxy of ours....
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This is a stupid excuse given to explain away poor implementation. What story? I can't have my character join a local faction where I imagine he grew up in. I can't gain a reputation in my chosen field. I have no exclusive missions/behavior/content based on the narrative i've created for my character through in-game actions. The NPCS and bgs reacts to me as if i was a nobody-npc. Even worse, because at least they can belong to factions and even have job monikers that give them certain privileges and other npcs react a certain way to them.
So no, it's less of a story you play out and more of a delusion you have with yourself to explain why there's so many missing structural pieces to the fundamental parts of the game.
edit: In essence, the lack of persistence of actions and the code needed to react to that history when appropriate is why pretending that you should play your own story and all that sunshine and rainbow jazz makes no sense. I can kill thousands of people and it means nothing to my character's reputation in the game. I can be a great miner, means nothing. I can be an awesome bounty hunter. Means nothing. I can join both armies, means nothing. I can rank way up in both armies and it again, means nothing to the bgs to the local factions or to any of the npcs who randomly are tasked to come after me or encounter me. Asking people to create their own character is great and all, if any of that matters in the game. The best we have right now is that if you frequent a given station and are allied, it will sometimes say that they have a port for you already.... yet FD still makes you request docking afterwards.. which lets that one positive fall on its face. O
Without persistence of actions, what's the point of creating a story? There's none. Your character has less functionality in the game than an npc when it comes to character building.