I wholeheartedly hope that Elite will one day have some kind of story campaign that is the same for every player.
There are dozens of cool features in Elite right now that many players only ever get to see in YouTube. For example, there are players who haven't experienced Thargoid interdictions or Thargoid refueling at barnacles.
There should be multiple single-player campaigns built around important historical events in the ED universe. You should be able to play a campaign where you are the first human to encounter a Thargoid in the modern era. That could be a great story - there could be a really compelling reason why you were out there and why you were the first person to "trigger" them. There should be a campaign around the Salome event. How many people even know that happened? I'm still not sure exactly how it worked in real time. But there could be a campaign around it with an interesting story.
These campaigns would be completely separate from the open-world game. It wouldn't be possible to earn anything in the campaign and bring it back to the open world. In effect, when you play the campaign, you'd be playing as a different person whose story starts and ends with the campaign.
There are many upsides to this idea and only one downside: development time.