I think its a very good idea that airplanes cant sink ships, and I believe that decision is gameplay-related, rather then reality-related.
Partly it has to do with the fact that modern ships in Civ-3 is generally more shield-expensive then airplanes:
Transport = 100 shields
Destroyer = 120 shields
AEGIS cruiser = 160 shields
Carrier = 180 shields
Battleship = 200 shields
Compare with:
Fighter = 80 shields
Bomber = 100 shields
Jet Fighter = 100 shields
Stealth Fighter = 120 shields
The only exception is the Stealth bomber, with a hefty prizetag of 240 shields, but that unit comes rather late in the game.
In addition to above generally more expensive navy shield-costs, remember that foreign warships outside your coastal cities, far away from their harbour-equipped homecities
cannot heal their battlewounds easily, until 5 hospitals (= 5 x 120 shields = 600 shields) + the small Wonder "Battlefield medicine" (= 500 shields) have been built. Even then the healing-advantage is on the coastal city-defenders side, because an naval attacker cant move and heal its injuries at the same time. It must be inactive for one turn (and therefore loose momentum).
Now - IF Firaxis really should let fighters and bombers sink battleships for example, it could lead to
big gameplay-unbalancing consequences. Remember that fighters and bombers cannot get killed
other then by counteracting enemy-fighters. Sending airplanes to sink modern ships would be a 100% riskfree operation, the way air-attacks are currently designed in Civ-3. Even a carrier + 4 jetfighters (= 160 + 400 shields) would be at an disadvantage, because the landbased defender, with lots bombers and jetfighters in his cities, would probably initiate the attack-wave in advance, in order to fend off naval attacks and transport-landing operations, prepard as he is. And the attacker has always an succesfull battle-outcome probability advantage against single unprepared (= unfortified) enemy-units.
One could argue to above; "Well, then they should add offensive airplane-attacking abilities to modern warships, as well". But then we are talking MAJOR unit-ability alterations, with unforeseen gameplay-consequences - requiring weeks and weeks (if not months) of inhouse playtesting all over again; for this single unit-ability alteration alone.
At the end of the day; would it really be worth it? 
Isnt their OTHER additions and feature-alterations the Firaxis-team can emphasize instead?.
If you want to damage enemyships lurking outside your coastal cities, you can bombard them with help of coastal fortresses, artillery and bombers/fighters, but if you want to kill them off completely you just have to build your own damn ships, for crying out load. Try to live (and have fun) with those rules instead, and stop whining about above airforce-vs-navy limitation, as if it is some kind of major gamebreaker. It simply isnt.
