The only reason their was a battle of Yavin was the death star had TIE fighters to take on the rebel fighters. The Trade Federation Battleships didn't do a whole lot of damage to the Naboo fighters. The droid fighters did the damage to the Naboo fighters and the Naboo fighters blewup the Trade Federation battleship.
You know, the space battle over Naboo is actually something I'd tend to cite as an example of a scenario in which dedicated carriers are essentially worthless. The Trade Federation "battleship," which is more along the lines of what would be referred to as an armed merchant cruiser in the real world (at least, using WWII terminology), is for all practical purposes invulnerable to fighter weapons; there is no evidence within the movie that the fighters so much as scratched the paint on the ship's hull until plot contrivance let a 10-year-old who shouldn't have been anywhere near the battlefield fly an essentially out-of-control fighter into a hangar bay and fire some torpedoes into an important bit of machinery which is for some reason exposed within the bay. If the only way your fighters can seriously threaten an armed merchant cruiser is to fly into its fighter bay and fire torpedoes at critical equipment which is for some reason exposed and unprotected within the hangar bay, your fighters do not represent a credible threat to the armed merchant cruiser, barring incredible incompetence on the part of the target's crew or incredible luck on the part of your fighters or both. If your fighters do not represent a credible threat to an armed merchant cruiser, chances are that they also do not represent a credible threat to a real warship; armed merchant cruisers are not generally known for having defensive capabilities superior to those of dedicated warships. The only evidence within the movie that the fighters actually represented a threat to the Trade Federation ship is that the Trade Federation ship actually bothered launching fighters to engage the attacking fighters, but on the other hand I'd not expect that the commanders of ships of the Trade Federation to be the most competent commanders for space battles.
Star Wars (well, the setting as depicted in the live-action movies; the EU is full of things not particularly well supported by the movies, and having not ever watched the animated stuff I cannot speak to that part of the franchise) is not a good setting to use to justify space carriers as the preeminent space capital ships; all six of the live-action movies provide far more support for the notion that whatever value fighters have in large-scale space battles is more in line with harassment and attacks on other light ships than in being a credible threat to capital ships. The ability of the Rebel fighters to threaten the first Death Star rested upon a single design flaw, the ability to hit something which is regarded by characters who should be knowledgeable about such things within the universe as a very difficult target, and the general lack of effective response by the station's commanders to the attack (yes, some defensive guns engage the attacking fighters, and considering that these are apparently anti-capital weapons rather than anti-fighter weapons, they don't do that badly, but the appropriate response should have been to launch fighters, and this is not done until Vader, who appears to be more along the lines of an important guest than someone who can actually order the onboard personnel around, orders his personal fighter force into play). Executor was only lost to that A-Wing because the Rebel fleet, which had multiple large capital ships of its own, concentrated enough fire to bring down the shields before the A-Wing crashed through the viewport, and even then it's unlikely that the ship would have been lost or even particularly badly damaged had there been time for the crew to regain control of the vessel before it crashed into the second Death Star. The ability of fighters to threaten the second Death Star rested upon its incomplete state; indications are that whatever information the Rebels had on what the finalized Death Star would have looked like, that information was sufficient to convince that what did the first Death Star in would not do for the completed second Death Star. If starfighters are, as you suggest, so powerful and effective in the Star Wars setting, well, the prequels provided a full-scale galactic war in which fighters should have had ample opportunity to demonstrate their power and effectiveness by virtue of the numbers of fighters employed on both sides and the large scale of the war, and yet the dominant post-war capital ships appear to have shifted away from the carrier and towards the battleship. Heck, if you accept the word of the Expanded Universe, the original trilogy's standard Star Destroyers (Imperial, Imperial-class, Imperator-class, whatever you want to call them) were already beginning to be introduced towards the end of the Clone Wars and supplanted the Venators (the only Star Destroyers I recall seeing in Revenge of the Sith) not long afterwards.
A history lesson is in order. World War 2 between Japan and the USA. Battleships were the thing to have in World War I but a few well placed torpedoes or bombs from a small group of planes on warships sinks them
Yes, we're aware that in the Second World War, carriers were the preeminent capital ship. It isn't at all clear that carriers, despite being the capital ship of choice of today's dominant naval power, will always be the preeminent capital ship. You know why carriers became the preeminent capital ships of the Second World War? Because they could effectively engage targets from far greater ranges than anything else available. This is no longer true; guided and homing missiles can in the present day engage targets at ranges similar to the effective striking range of modern carrier-borne aircraft, and ship-launched missiles are at present about as effective as the attacks of carrier-borne aircraft. Missile cruisers may well supplant the carrier as the preeminent capital ship at some point in the not too distant future. Or they might not; I'm no more blessed with knowledge of the future than anyone else is.
Your position essentially boils down to "because modern naval carriers have been the preeminent naval capital ships for the past ~75 years, vessels similar to modern naval carriers will always be the preeminent capital ships of any force which is remotely based upon the present-day navy." Allow me to explain why this is wrong by way of an example. If the present day were, say, 1915, the preeminent naval capital ship would have been the battleship. Ships similar in nature to the battleship would have been the preeminent naval capital ship for more than two centuries. By the same argument that you make for carriers, battleships should therefore be the preeminent naval capital ship in 2015, and would also be the preeminent capital ships for the space navy, despite the space navy operating in a completely different environment. We can go back even further in time; the trireme and ships like it were the preeminent naval warships in the Mediterranean for ~500 years, and various types of oared galleys whose primary attacks were ramming and boarding continued to be the predominant warships of the Mediterranean for another one and a half thousand years or so. If this game had been introduced in the 15th century Mediterranean, then, 2000 or more years of historical precedent would say that ramming and boarding should be the primary modes of attack for the capital ships of the future. Your argument takes no account of how technologies may evolve. It takes no account of how the environments differ. It takes no account of how people's views on what constitutes acceptable losses may change. Your argument is entirely based upon historical precedent in an environment which bears little resemblance to the environment in which the game's large and small warships will operate. I'm sorry, but this argument is deeply flawed.
Additionally, the mere fact that carriers are at present the preeminent naval capital ship and have been since the Second World War provides very little information about what the preeminent space-going capital ships will be ~250 years from now. Space is a very different environment from the ocean. Aircraft are considerably faster and considerably more maneuverable than warships; starfighters are not guaranteed to be considerably faster or more agile than space-going heavy warships. The starfighter may well be to the space-going capital ship what the American PT boat or the British Motor Torpedo Boat or the similar craft of other nations was to the battleship in the First and Second World Wars, and neither PT boats nor their tenders, despite PT boats and MTBs being credible threats to capital ships under the right conditions, have historically supplanted the battleship or carrier as the preeminent capital ship of its time.
Beyond that, though, is the question of whether or not any of what you've written even matters. Galactic Civilizations III is not a game which is trying to portray WWII-era naval combat in an accurate manner, nor is it attempting to portray modern naval combat in an accurate manner. Nor, for that matter, is the degree to which Galactic Civilizations III accurately reflects the state of modern naval warfare particularly pertinent to the question of whether or not Galactic Civilizations III carriers are overpowered, nor is this pertinent to the question of whether or not it makes sense for Galactic Civilizations III carriers to be overpowered. Galactic Civilizations III carriers (which are space-going warships, not sea-going warships) are, when properly designed and when benefiting from the proper bonuses, effectively uncounterable except possibly by other Galactic Civilizations III carriers. Whether or not this is 'realistic' is immaterial; whether or not this is an enjoyable or desirable state is material. The fact that this is the case greatly reduces the player's freedom of design when creating ships, at least if the player wants to create competitive ship designs. In my opinion, and I rather suspect in the opinions of many others, this is detrimental to the game.