This is actually making me start thinking about game design theory. (I'll acknowledge right up front that this is probably never going to happen, but it's fun)
So, right now, there's seven types of ships in use(Attack Destroyer, Defence Destroyer, Missile Cruiser, Aircraft Carrier, Helicopter Carrier, Attack Sub, Nuclear Sub) and six things they can carry(Seals, Interceptors, Fighters, Helicopters, Missiles, and Missile Interceptors) to form naval groups.
What I'm thinking is treating ships like limited bases, with the ability to carry units within them. Those units can then fight if they wish, or the ships can fight directly. For purposes of simplicity, and allowing realistic numbers while still working with the SC combat model, carrying capacity is aggregated - if a fleet has four carriers that can each carry 100 planes, it can field a single 400-plane attack wing if desired.
Aircraft Carrier - Carries 100 planes and 100 helicopters, provides air cover to the fleet.
Helicopter Carrier - Carries 100 helicopters and 10 Seals, used mostly for land attack.
Nuclear Submarine - Nukes cities, hard to detect/destroy. Should have a fairly short range, to allow detection by defenders without searching all the oceans of the world.
Attack Submarine - Carries 10 Seals. Very effective against non-destroyer ships, hard to detect/destroy.
Missile Cruiser - Carries 100 missile units. Used for long-range bombardment and naval surface warfare.
Destroyer - Merge the two types into Defensive. Primary anti-submarine screen, but also okay against surface ships.
(Renamed from "attack boats") Assault Ship - Carries 100 land units and 10 Seals.
Of the carried units, all but Seals stay as-is. Seals are no longer ship-to-ship commandos(which is redundant and unrealistic), but instead work much like Special Forces. Also, add ASW helicopters(used for detecting and hunting submarines, can get the 3-wing federation air defence thing going on) and Naval Bombers(like Precision Bombers). Naval aircraft and missile units should generally be slightly weaker than land-based equivalents, and should be usable on land(this is particularly important in the case of ASW helicopters).
When I say subs should be "hard to detect", I mean that they shouldn't be visible or attackable at all without some kind of ASW assets in the area(ASW Helicopters, Attack Subs, or Destroyers should be the only things that can damage a submarine). Nuclear subs should be the scariest of the strategic weapons, much like they are IRL, because they're hardest to counter, and they'll be one of the primary impetuses for having a navy at all. The other big one will be Assault Ships, of course.
An interesting note. Under this design, all surface ships are defensive. Their carried units can attack, but they cannot. (This is fairly realistic, actually - meaningful direct fire from surface ships is pretty rare in the modern era)
These ships can now be combined into the following fleets(default compositions listed):
Wolfpack: 60 Attack Submarine (Used for attacking fleets)
Nuclear Submarine Group: 5 Nuclear Submarine, 25 Attack Submarine (Used for bombarding cities)
Carrier Battle Group: 10 Aircraft Carrier, 20 Missile Cruiser, 70 Destroyer (Used for naval air superiority)
Surface Warfare Group: 40 Missile Cruiser, 60 Destroyer (Used for attacking fleets)
Invasion Group: 10 Helicopter Carrier, 20 Missile Cruiser, 30 Assault Ship, 40 Destroyer (Used for putting land units onto hostile shores and aiding them when they're there)
This is all spitballing, of course, but it seems to make a fair bit of sense to me.