My contention against the carrier is that it lacks stopping power and is prone to depletion. A battleship can carry a lot more shells than a carrier can, and won't be in a position where it can't launch enough shells to get through the enemy defence. Sometimes their new fighter will surprise you, sometimes they reposition their forces to overwhelm a theatre, Sometimes they have a new A.A. turret that tracks your aeroplanes better than they can evade... Sometimes your anti naval aeroplanes can't stop their boats... Sometimes you can't press an advantage because if you get too close you are toast, so you just have to sit by and watch them scamper away.
According to Wikipaedia, The Musashi took 19 torpedoes and 17 bombs(an even three dozen) and damage control efforts continued for almost four hours before she sank. While The Yamato was basically in a shooting gallery, all attacks against only a single side of the vessel. It is the worse example. I do not have data on running costs but I cannot fathom that the costs of a battleship that floats at, say, 40 knots, is going to compare to a scout cap, flying, at five times that speed. Battleships and carriers both have heavy machinery and light machinery, but carriers require maintenance for numerous fighters, which is technical work, and have frequent use of lifts and such with very repetitive and ungainly vertical actions, along with odd bits and pieces like braking cables and aircraft conveyances. Battleships tend to have more stable circular actions for things like turrets. Certainly, when a battleship breaks down it is very expensive, but a carrier has its own share of expensive parts, and breakdowns seem morel likely given their engineering difficulty(circles are easy because motors make circles...). But history is not something that I am trying to argue here, as this is a game thread, so such things are not relevant except as illustrations of the game's hypothetical scenarios.
If the destroyers see the enemy then it is too late to launch a counterstrike. And I am not talking about carriers being personally overwhelmed and the ships being crippled, I am talking about carrier-launched aeroplanes being overwhelmed and unable to take action. Carriers have a clearly superior range and volume of force projection, and the advantage of scouting and attacking without revealing their position. I don't doubt that they are 'better' but there is still the issue that being able to throw actual shells at that distance would be more immediately threatening and more difficult to stop, as shells cannot be shot down and have a much higher velocity. Battleships DO have advantages and those advantages CAN find opportunities to present themselves. By all means the carriers should be the basis of fleet doctrine, but destroyers and carriers both lack the ability to stop a determined task-force of similar proportions from attacking them. A battleship can politely inform such a force that no amount of air cover in the world is going to stop a shell that is on course for their deck and that they really can't hope to see it prove ineffective as a battleship might against an air-dropped bomb. Just a handful of really big guns can turn a massacre into an orderly withdrawal or a harassment into a determined assault. Or it can turn that incident where an enemy destroyer-group or small force of aeroplanes finds you while your own aeroplanes are off doing something and your destroyers are forced to sit by and watch torpedoes sink your clumsy carriers or jump in front of them and get sunk themselves. A battleship can sink them from outside of torpedo range and shield a carrier with a somewhat decent chance of surviving.
We don't NEED battleships, but to consider them useless is, in my opinion, misguided.
As for submarines, I could se them gaining a bonus against naval advantage and if we are modest in our demands for dive-depths and agility then it should be possible to transport pretty much any tank or aircraft we would be likely to field, along with a chance to drop heavy land-forces undetected, for some of the advantage of a paradrop with much better equipment(Though the same crippling lack of support). Combine the two and you can drop paratroopers to take their airfields, sneak Tigers and heavy A.T. guns by sea to hold them, then land all the supplies and reinforcement you like while your conventional forces push in from the front lines. It is an ambitious idea, but I would expect a submarine with a capacity of three would be more plausible than an aeroplane with a capacity of 2, and far less likely to be shot down as a big, slow target that is dancing around up in the sky where everyone can see it.
I do feel that the aeroplane is a more sensible option, but that just goes to show how embarrassed we should be for considering it...