Back on topic: Aquanox is an FPS disguised as an underwater sub simulator.
It's predecessor Archimedean Dynasty is the real deal: arcade simulation of advanced submarines in a post apocalyptic underwater setting with a plot and complex missions.
(Nowadays PCs are fast enough to play it well on Dosbox).
There are a number of concessions I'd make for gameplay:
-Subs should be able to dive a lot deeper.
-Subs should be faster and steered like planes. (There are such designs, heck you can make your sub a lot more nimble if you rely on the Bernoulli effect (lift) instead buoyancy).
-You could make bombers buoyant designs and fighters lift designs. The later have to keep moving to maintain depth, but are faster and can dive quicker. Buoyant designs can rise faster.
-Add thick armor, so subs could take a lot more pounding without being crushed.
-Actually fighters and bombers could altogether dispense with air if they used oxygenised liquid breathing systems - so could capships, but let's say people can't be immersed in the stuff too long or their skin dies (actually true), and capship needs time to "flood all compartments" with breathing liquid.
-Add some fluff about super cavitating drives (your "jumpdrive") on big carriers with smaller subs as escort.
-Add green lasers for close in zapping, gryojet guns for medium range spray & pray, super cavitating guns for long ranged sniping and torpedoes for long ranged volleys and super cavitating torpedoes as capship weapons.
-Normal torpedoes can be shot down. Same goes for supercavitating torps, but they're really fast.
-Normal torpedoes could be "plentiful" (half a dozen on a fighter, two dozen on a big bomber), while supercav torpedoes are big things, a fighter may carry two, a bomber six.
-Small supercavitating torpedoes could be the "new weapon" of the game...
-...that you can counter by super cavitating gun turrets...
-...or explosive mines since:
-Super cavitating weapons can be destroyed by shockwaves as disruption of their cavitation bubble results in massive forces acting on them. (These forces also arise normally, but only to the carefully designed cavitator surface while their bubble is intact). So "flak-burst" can protect a ship from these weapons.
-You could also deploy buoys that release a gas curtain. Then the attacker has to either dive below the curtain or use special multi-stage weapons that use conventional drives to cross the curtain. (At that moment they're slow enough to shoot down).