I read this book on the British Navy it went something like this...
(it was called To Rule the Waves: How the British Navy Shaped the Modern World by Arthur Herman. Good read)
The West Country had this maritime tradition and then came Drake and the Spanish Armada and the "Age of Fighting Sail" and blah, blah, blah. And then the Americans built a ship out of steel (the Merrimac or Monitor) and from there, naval warfare was revolutionized going from wood to steel. Against the ships of the day, cannonballs would just bounce off if you had enough armor. Technology was improving pretty quickly and people would make bigger guns (rifled guns) and biggers ships and so on. Countries (England, America, Germany frontrunning, Japan later and maybe a little Russia too) would just keep, one-upping each other by building the biggest baddest "Dreadnought-class-Battleship" they could. You could just park this thing in someone's harbor and this huge Battleship would be an awesome sight. But then something happened technologically that changed the fate of naval warfare. you could just get a submarine, or a ship, and later even an airplane to drop a torpedo at these huge ships and sink them like that. A couple million dollars (or whatever) and a year+ of labor gone like that. The Battleship (and you could call those wooden, sailed ships in the age of napoleon battleships) that ruled the waves for so long were obsolete. And then another HUGE change to naval warfare was the airplane. If you didn't have control of the skies you were at a disatvantage.
So now, in modern times what we have to replace the "Battleship" is the whole package so to speak. You need Destroyers for sub defense and cruisers with big guns and ESPECIALLY the carrier for air support. In these modern times, the aircraft carrier is the central piece to a modern navy. It's the thing you park in someone's harbor when you want to make your presence known. The carrier has become the modern "Battleship".
In CIV 4 terms, well, you're working your way through the ages and you're at whatever point your at, but if you get to modern times (i.e. future tech) and your enemy's is competant and equal your power(i know the AI sucks), the carrier plays an important part. You still use battleships for sinking ships and protecting transports but if you wanna land an invasion, the carrier with intercept fighters is gonna keep your ships from being sunk.
Maybe no one gets to this point (i haven't really) but i think the game is balanced well in this way and the carrier definately has its role in the whole rock-paper-scissors way of things.