What is the reason for passing time while docked? Trying to be realistic in a game that violates reality in several ways? Plausibility may be a good reason, but for that, a broad and simple solution that can plausibly explain most if not everything should suffice.
I bought up one day in Endless Sky because it seems simple and works there as plausible explanation for whatever the player does while docked. Some activities may take more or less a day. (In ES, you can buy and outfit a thousand Star Barges for whatever silly purpose. Would it take more than a day? I don't know, but it doesn't matter that much. Should it take a whole day for quick refueling stop for one ship? Don't know, doesn't matter.) Yes, Starsector is not the same (kind of) game, but similar enough that the concept that works in ES can work here too (at least until maybe Starsector gets outpost building). Both games have stations player can dock at. Both games let player buy or sell commodities or ships, or maintain your fleet. Both games are similar in feel. Maybe if Starsector supports outpost or other empire building aspects, gameplay will diverge from other similar games.
Yes, player can get so overpowered in ES as to snuff out the Archons like nothing. That is probably comparable as player getting so overpowered here that he can solo super-simulator fleets with a battleship without taking hull damage.
That said, you are not allowed to dock at enemy stations in Endless Sky (with exceptions for some missions). In Starsector, you can dock at an enemy station with the largest, most flamboyant war and/or trader fleet if the enemy is sufficiently distracted (and transponder is off). Spending much time at a vengeful enemy station while they are after your head does not seem very plausible. If spending time at a enemy station is implausible, it is a good thing transactions and outfitting are instantaneous.
If outposts and maintenance becomes a thing, time will probably become very important.
the underlying thing I don't get is: what Alex is trying to do with this game? On the one hand, he goes through the trouble to simulate an entire economy and has all these procedurally generated NPCs that maintain a reputation status with the player, but then there are all these concessions to casual gaming and shootemups that jerk you out of the immersive dorkyness.
This is not a problem for me. Starsector is a game first and foremost, not an interactive novel or movie. Do people get Starsector for a compelling story? to blast ships?