First of, apologies if this has been suggested many times over - the forum is too big to thoroughly search through (and simple text search doesn't cut it).
Starsector is a rough diamond, which is already great, but I feel there is still one - but crucial - element missing from it: our in-game actions don't really matter, which makes it somewhat boring to stay engaged beyond early game.
So, @Alex, please, make our actions matter. (The rest is superficial stuff: rebalancing ships, adding graphical effects, adding colony buildings etc.)
Two obvious culprits here: a) absence of a greater purpose and b) respawn. These two are closely related. Nexelerin kind of, sort of, partially, in an awkward way helps with, but doesn't fully solve, issue A. So the greater purpose could be help our faction win, e.g., by having 51% of sector GDP, or 51% of all habitable planets, or being first to unlocking some super tech, or something similar. (I personally prefer GDP.)
If Starsector is about creating our own story, this all would fit right in: we can help our faction by fighting alongside their official military in conquests, or by raiding rival factions to limit their resources, or exploring outer reaches for new tech/blueprints that helps our faction (if we choose to give it to our faction instead of beelining for the black market), or by finding great planets for our faction to colonize, or maybe something else.
This brings me to issue B. I absolutely loathe simplistic respawn - and I think most of the readers of this post do too. Spending time and effort winning a tough battle only to see AI respawning another stack makes me wonder what was the point of my effort. Please make respawn more intelligent, e.g., by introducing the notion of GDP - the resources that a faction can dedicate to 1.1) building up a military to attack or 1.2) defend, 2) investing in their economy to get more resources next month, 3) sending out exploration parties to the outer reaches, 4) setting up raiding parties, 5) bribing pirates, 6) developing new ships/weapons, 7) colonizing new worlds,

something else.
If we defeat a large enemy fleet, it's a huge loss for them and they need to recover. If we find a useful blueprint, it helps our faction military in the future. If we find and report a sweet planet to our faction, it boosts the economy in the long run. This would make our actions matter, and make us feel a useful part of a larger effort.
As a final point, Nexelerin's idea of diplomacy is great. If our faction gets stronger, others should be prone to team up on us, otherwise it snowballs and leads to victory too quickly.
That's all. @Alex, thanks for the game.
P.S. please implement an option for me to limit the number of hours I play a day - so I can set it in the beginning, while I still have the willpower to not skip sleep...
EDIT: I'd emphasize "make us feel a useful part of a larger effort" and add "a tiny useful part of a gigantic effort/struggle". Because currently we really aren't: 1) stomping out pirates doesn't matter - they respawn right away and their activity affects the sector only mildly (nothing ever descends into complete chaos); 2) stomping out Ludds makes even less sense - for the same reason as Pirates, but also because they aren't well fitted in the game/lore besides being Pirates--; 3) exploring outer reaches doesn't matter - other factions don't care about planet surveys I sell to them, it's just an item to sell, and blueprints don't do anything meaningful besides adding one more way to get a ship in mid/late game; 4) raiding trade convoys doesn't really matter - they contain little loot that barely covers the costs of fighting and these fights are boring beyond early game, plus factions don't really suffer from loosing these convoys; 5) shuttling goods to struggling worlds with a deficit doesn't matter beyond making a bit of cash - and gets boring quickly; 6) Clearing out Remnant from a system doesn't matter - nobody will colonize those worlds anyways, and AI cores are only good for slightly improving your reputation with a faction or selling them and seeing them sit in that market forever unused;

And don't get me started on the procedural missions - shuttling goods is just about watching space travel sequences (graphics are absolutely gorgeous, but it does get boring) and makes no in-game impact, and hunting down somebody/bases is just another way to shepherd us into a space battle, the outcome of which again makes little in-game impact. 9) Conquering a world/planet does make an impact, but it's the only way to make an impact, and it gets boring; I become a wrecking ball in mid game and just run around conquering worlds. I'd prefer to be a tiny part of the Sector for much longer, and affect it in other ways than repetitive, mechanistic conquest, and only become a wrecking ball at the very end if ever.
For the game to not be boring beyond early game, the Sector needs to be dynamic and we have to - I'd even say, must - see how it changes based on our actions.
Addressing some of the arguments: If Starsector is about space battles, it was finished long ago and Campaign isn't needed. Just selected ours/opposition ships and keep blasting. If Starsector is an interactive story-telling device, it'll be done with version 1.0 - I'll blitz through story points/missions, admire a possible final cut-scene and delete. But then why have Colonies, Factions, Reputation? It's weird to have these classical 4X elements, while desperately trying to not be a 4X game.
Btw, Colonies are my least favorite part of the game. They are a nuisance, especially stomping out incessant pirate raids and Ludd infiltrations (both of which respawn right away), and defending against AI inspections. If I play again, I'll have no colonies.