Let me clarify 

The story would be a DLC and therefore optional.  It would be a DLC of substance and depth, new faction, new ships, new nodes and story.

The story would not impact on existing factions.  It would be a background dynamic story that unfolds throughout the game session.  It would react to player choices. An example would be if an empire faction is eliminated then the story would reflect this having different endings or narrative, this would increase replay ability as the story would be different depending on what happens in game.  If a player uses planet killer weapons then a story could unfold around ecological disasters. If a player builds an observatory, then new discoveries could be made. Relic systems could be introduced, offering empire wide bonuses and new emergant star systems to investigate and exploit. Multi player dominance will restrict creativity as all games ultimately look and play the same based on the premise that all things have to be equel, life is not like that.  

Yes this game is not an RPG and I am no way suggesting that it should be.  Campaign story can be told within the scope of this game.  The "Vortex campaign in Total war hammer 2 ", represents one of the finest campaign examples in recent years.  It does change the way you play the game without intruding upon player imaginings or freedom.  It offers new game play mechanics that shake the formula up.  I often wonder what Total War would be like if they made a space 4X game, probably perfect.  Suggest opening up a dialogue with amplitudes sister company on this, just to get some ideas.

The lore and history of the endless could be told quite effectively with art and visual assets.  It does not need to be linear, many games are choosing story to be told in a more flexible way. New game mechanics can be introduced.  Introduction of new factions or star systems could be created in mid game.  

The issue with quest stories are that the player often gets blocked from completing the given quest.  I have played through whole games without finishing some quests.  This blocks the story and is in danger of becoming redundant.  

I feel that ES2 is swimming in the shallows, not wanting to be adventurous enough.  Yes the content is there but adding more factions and ships is ultimately playing it safe.  This game needs to evolve to survive and flourish.  Developers need to be pushed and tested. The best single player games are doing this.  Multi player is a very different fish.  I suppose I am trying to nudge ES2 into a more single player arena, otherwise, like most multiplayer games, it's shelf life could be limited in the long term.  

My experience is that a creative team needs meaty direction, new and uncharted concepts to flourish.  If not then they get stale and the game starts to reflect this.  Leadership and direction are key here.