In addition to fleshing out the narrative potential of the Sins universe, a campaign would also provide some continuity for those of us who loving name each of our capital ships, planets, and starbases, and imagine their crews, citizens, and commanders (respectively) gaining experience, suffering through events, and either becoming stronger for it or going heroically to their deaths. When a game of Sins is over, it's over. You might name your new capital ships in your next game the same thing, and follow the same ability upgrade path, but it will never be the same ship.
Several people have pointed out that a "progressive unlock" system, as generally seen in RTS games like Starcraft, would not work well for Sins. Completing any map, regardless of its size or victory conditions, would be nothing short of tedious with only a handful of light frigates, one capital ship, and a tier or two of research. However, on my view, a campaign for Sins could never be about taking things away; it would have to be about adding things, which I acknowledge is a technical obstacle as much as anything else.
For example, adding "hero units" would allow a campaign to follow a handful of characters (as all engaging narrative must). Star Wars: Empire at War (for all its numerous flaws) did this well, both in its main campaign and open-ended "conquest" mode. For example, playing as the Empire, you could build regular old Star Destroyers, but you also had Captain Piett in his ship (the Accuser, I believe)? But then you also had more civilian characters, such as Mon Mothma, who could be stationed aboard any ship, structure, or planet. So as the TEC, you might have a TEC captain or admiral commanding either a dedicated flagship or moving between other capital ships, which you then might be able to take with you to the next scenario.
This is a galactic war, and it makes sense that it would be fought over several systems. I don't see the "beginning to end" process for each map to be a hindrance to the formation of a campaign: you, as Fleet Commander or Supreme General or what have you, are given command of a particular sector during a particular stage of the war. You are either victorious or you lose, and then you move on to the next sector, possibly taking your flagship and/or hero units with you.
I'm not saying any of this would be easy or even immediately practical... and there are lots of other ideas that other fine folks have suggested over the years on the topic of the "campaign question." But my point is this: it's not impossible. Sins is too good of a game to be incompatible with a single player (or, perish the thought, co-op multiplayer) campaign.
Are we going to get one? I don't know. Frankly, I doubt it. But I think when we unwrap our Titan-class ships and new capital classes in Rebellion, we'll forget the issue. At least for a time.