I'll start by saying I think it's generally understood that current expeditions are somewhat of a placeholder endgame that will be expanded upon, and so it's expected that they aren't super polished.
Long winded discussion of the gameplay function of expeditions:
My understanding of the gameplay function of expeditions in the current game is that they are a mechanism primarily to impede the player from setting and forgetting their colonies for passive income.
In my opinion, this should be the role of pirates, not factions. Pirate raids, pirate activity, and pirates bases are enough to force the player to invest in defenses and require player actions to get colonies off the ground. In my opinion, it's fine if the player can get their defenses to a point where they can stop paying attention to their colonies, as long as it is sufficiently difficult and expensive to get to that point. In other words, it should be 'upfront' difficulty rather than 'grindy' difficulty.
One of my biggest issues with the current end game is that expeditions are mostly just an annoyance once you get max defenses up, it just becomes a reputation tax. I think this is both unfun, and also somewhat strange from a 'lore' perspective (why are the factions chill with sending massive fleets endlessly to their deaths as long as you do one delivery mission for them each month). I think having a mechanic where you have to perpetually do trivial tasks in an endgame is just generally bad. The price for having colonies should be in the difficulty of getting them to that end-game power level IMO.
My goal with this suggestion is to come up with a system where expeditions are a more 'upfront' cost to establishing colonies that is difficult in a fun way, and also makes more sense thematically/within the lore.
The suggestion:
Expeditions are one time events for each factions. Perhaps once per colony per faction, or once per industry type per faction, but some small finite number of times.
When you initially reach the threshold of production (or free port or whatever) for triggering an expedition, you are given the option to shut down the industry, pay some (large) portion of your income/production to the faction every month, or refuse. Paying a fraction of income should be a way of delaying the expedition i.e. you can stop paying at a later date and trigger the expedition then. It should be enough of your income that you really don't want to do it forever. Maybe the faction could demand more and more as you grow or something. Once you refuse, there is a delay before the expedition is sent, and maybe you can leverage contacts to get more info about when it will happen and what it will entail.
Since the expedition is a one-time thing, it should be a 'boss battle' type event. I personally thing that the 'endless waves of capital ships' type stuff from nex is not that engaging, so what I would propose would be that each faction has a unique boss ship that only gets sent during expeditions and isn't recoverable. The expedition is trying to take your colony from you, so you need to win to avoid losing the colony. The idea is that you really shouldn't be able to avoid losing your colony without fighting yourself, and it should be hard, even for a mid-late game fleet with a max level station.
Once you defeat the factions expedition, they should stop bothering you because you stood up to their best shot. They also probably shouldn't like you much anymore, but that's more a reputation thing than an expedition thing. Maybe there could be an alternate path with a commissions faction to avoid expeditions or something.
The idea is that the expedition system limits the income you can get from colonies until you can beat the bosses. You have to keep them small/under the radar, or have your income heavily reduced if you can't beat the bosses. It also creates a situation where it's actually reasonable to make sacrifices/lose ships to win, which is something I really want to see in the game. Ideally, it adds a big upfront dose of difficulty to making super colonies, but eliminates the annoying long-term rep tax.