Kryo has pretty much laid down the law, but a few comments on the weaknesses (as I perceive them) on military starbases now that the ball has started rolling.
You misunderstand how Military starbases work. Military starbases are not intended to nor to they actually exert any control or power of their own.
This is obviously a fundamental design decision and, as such, not something that is up for discussion where GalCiv2 is concerned - but, I might venture, it
might be worth reinvestigating the issue for a potential GalCiv 3.
Starbases do have the potential (and they are very obviously often seen as such by the players) to be the "fixed fortifications" of space, something that is an alternative to fleets. As is, being merely "fleet boosters", they put the focus on the micromanagement of fleets for defensive purposes. Conceptually that ties in very nicely with ships in orbit and planetary defenses coordinating ships in orbit ["He who owns high orbit owns the planet and can rain hell down on it with impunity"] but in practise, in the game, it does not work out that way. The player will always be better off gathering his ships in fleets and hunting down intruders within striking range than garrisoning every planet - or even garrisoning the most important planets. The faster the ships in general (which increases with tech), the
less valuable high-level end-game defenses are. Couple it with interface annoyances such as fleets being broken up if the enter planet orbit and need to be reassembled into a new fleet when leaving and you are in the interesting situation that, overall, the player is better off not garrisoning a planet, not falling back to defend threatened planets, and not wasting tiles on building planetary defenses in the first place (more economical tiles allowing better tech/more ships over time) being a better defense.
In practise... If you ever are in a situation where a military starbase would make the difference between success and failure on the defense on a strategic level, you have pretty much lost the game, since any competent enemy will blow the weakly defended starbase out of the sky first.
In face, one of the weaknesses of the military AI is that it does try to protect its planets in the way it should, conceptually, and being hammered for it because the game rewards bypassing the fancy stuff and concentrating on swift fleets.
What is the importance of this for military starbases? Well, let's look at your list.

Their power lies in the 'ship assist' modules, which makes any friendly ships in their radius more powerful (especially very small ships, which are weaker to begin with); a planet *must* have ships in orbit in order to prevent invasions, and military starbases can make even the weakest defender put up a good fight. Otherwise, a military starbase acts just like any other--it sits there and only fights back when it is directly attacked.
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This is obviously true, isn't it? Well, not it
ought to be in the game, but it is not. That small ships are weaker one-by-one than large ships is certainly true, but due to the way that weapons scale by hull size, it really isn't the case where it matters. I swear, the ship designers in my game would probably end up with more powerful capital ships if they would just superglue tiny fighters with lasers mounted unto the hull instead of trying to mount lasers in the apparently HUGE mounts that large ships use that provide the same damage as lasers mounted in fighters but take up much more space... Heck, using small fighters glued to the hull as independent turrets would make a capital ship much more lethal, assuming a decent superglue, that is. Even if the glued-on fighters got slaved to fire salvos on one target at a time, just like the 3 km+ huge capital ships already do, it would still be more powerful.

As far as logistics and offense are concerned, small ships aren't weaker - they are stronger, and this is what is boosted the most. Now, the question must be asked - what, exactly
is it that the military starbase offers? Is it really increased efficiency of weapons on your side or reducing the enemy through strengthening/weakening of beams, the increase in speed by giving an extra boost with tractor beams &etc? If so, one must conclude that the bureau of weapon design in the fictional universe are numbskulls - if they are capable of providing that sort of effect so far from a starbase, it should be possible for them to provide direct military assistance as well. Let's use those tractor beams to shake up the enemy ships rather than merely slow them, eh? Or how about seeding missile pods slaved to the Starbase's control through its zone? Is it rather enhanced command and control? (then it should probably be percentage based increases)
The military starbase in GalCiv2 as of 1.2? A useful "assemble on the spot to boost my cheesed tiny/small fleets as I first blast into your system to destroy your assembled fleets" kit, but not much more, and poor at that unless you choose to focus on the small-ship approach. Even if loaded up with self-defense modules, its low hitpoints makes it too weak when attacked to be a reliable defensive fleet booster, its actual fleet boosting effect drops percentagewise as tech increases (though the cost to keep it alive with new modules increases) and it certainly is not much help defending planets compared to the ships you could have gotten for the same price (including maintenance). (And, of course, if you actually want to protect your expensive military starbase, you need to protect it with a fleet of its own)..
Is this necessarily bad? In my verdict (though yours might reasonably differ), yes. It could have been so much more. They could have been good enough that the huge costs of building a fully upgraded military starbase would sometimes make military sense. As is, military starbases are something to drop down for convenience during invasions with a minimal number of self-defensive modules (as they make no real difference to survival except in the very early game), and a luxury that the AI can waste some of its precious resources on to little gain, thus handicapping it compared to the player.
But it could have been so much more.

...It could have had an integral fighter wing (logistics/2 tiny fighters with 1xcurrently best researched weapon) that would fly out and autoattack enemies within range, automatically replenishing logistics/6 fighters per turn. That's an actual zone of control. (So sure me

Much better than me maintaining fighter patrols and manually doing it on all fronts

)
...It could have generated mines throughout its zone of control (one mine at random per turn, say

) Ok, strictly speaking the UP might want to have something to say about THAT sort of idea, especially if somebody mined the trading lanes.
...It could have gotten, say, 100% more hitpoints per level of Starbase Fortification tech making it a durable structure that it might actually pay to upgrade defensively since it would be able to survive attacks by weak enemies, even as tech and damage increases, unless it got REALLY unlucky. (Not every fleet has a Luke Skywalker to take out a heavily fortified military installation)
...It could have gotten a level IV and V of Starbase Fortification at high research costs, allowing Starbases a chance at keeping up with high-tech weaponry. Hey, we are talking about a base bigger than most ships and presumably with much better energy-generating and repair capabilities.

...It could have an impact on planetary morale (you are defended!)
...Instead of increasing/reducing speed by a fixed amount, it could have affected the cost of moving a tile on the map. That's nasty, effective, and means that it is actual passage through the zone of control of the starbase that matters, not whether you start your week inside its zone of control. It also scales pretty well with increasing techlevels.
...Or it could have been enough better at what it is currently intended for it to be worth the price in more cases than is currently the case.