The overarching benefit of carriers is the stackability of fighters.
Most non-carrier ships require line-of-sight and much much shorter ranges to inflict their damage, but carriers can do so from comparitively absurd ranges. Combined with their AI behaviors, fighters tend to form swarms that can utterly swamp the vast majority of ships.
A mental expertiment: Although it's not an exact comparison, mentally convert ships into their deployment costs, and estimate how many deployment points you can have focusing on a single target simultaneously. Carrier ships obviously allow a much greater concentration of deployment points on a single target, and any damage they incure is simply replaced over time. Although carriers tend to have much less flux dissipation, their fighters are also part of their defenses too.
I agree that carriers present a neat dynamic to the game, although I also agree that they're a little too powerful in the current meta. (Personally I think their ranges are too big, and should be more comparable to the other offensive options. The stackability of fighters is their source of imbalance, so reducing range would reduce the overlap of multiple carriers. With the exception of the Heron, the reduced speed of carriers is a good balance IMO. Similar to lowtech ships, carriers have high alpha, high durability, and slow recovery.)
Balance issues aside, they can be countered, as previously discussed in this thread.
Something I forgot to mention, however, was hotswapping loadouts before your fleet comes into contact with the enemy fleet. It's not often that you don't have a chance to pause and enter the refitting screen before coming into direct contact with enemy fleets, so it's possible to make some changes to your fleet to counter the enemy fleet once you see their composition. IMO, the initial loss of CR is well worth it if you can minimize your losses in combat due to the enemy having the rock to smash your scissors. You can't completely revamp your ships, of course, but changing a couple weapons is doable and could have a huge impact on the battle. This is especially useful when you're going into an enemy faction's space and know you'll be fighting fleets with specific themes since you'll only need to pay the cost once for a bonus to your effectiveness in all the following battles.
I used to do this in WoW all the time. I carried 1 to 2 bags worth of extra gear, and had a mod that could swap all my gear instantly (out of combat). I would usually lose some HP and MP from swapping gear with different stats, but the difference in gear was well worth the change. I could instantly swap my gear so that I had enough regen to make even druids cry, or be tanky enough to make rogues whine OP. I did the same for all my characters and was always at the top of the lists in terms of effectiveness in battle.
In other games like Borderlands, it's pretty much necessary to have gear suitable for all targets. If not, you're gonna have a bad time.
Oh, and another useful tactic is to deploy only the most impactful ships when needed, and then retreat them once they're no longer needed. For example, when facing mid-game and end-game fleets, start battles by deploy ships specialized in evaporating frigates and then retreat them once that's mostly done with. When carriers show up, field your anti-fighter forces. When the enemy carrier force is no longer at critical mass and effectiveness, retreat your specialized anti-fighter force. Don't just field generalized ships and wait for them to blow up before replacing them. Retreating ships earlier and fielding more shipsoverall is less expensive than blowing your ships up and recoveringthem afterwards...provided they pop up as recoverable.
These specialized 'forces' are usually just a couple ships, for me. Some ships and loadouts are even effective as a combination anti-fighter + anti-frigate. Anyway, just saying that trying to equip your whole fleet to be able to handle everything, anytime, with only a single loadout and fleet strat can often work against you. I'm usually against the "Jack-of-all-Trades = poo" bandwagon because there are plenty of effective JoaT specs in most games (even if there are even more useless JoaT specs), but IMO, your fleet will be more effective as a whole if you DON'T try making all your ships JoaT boats..