Why fuel? Isn't the point of carriers that they carry?
Indeed. Fuel is used strictly for hyperspace travel and has no effect on combat. It's reasonably safe to assume whatever combat energy, materials, ammo and fighter squadrons that go into battle is coming out of their supplies.
Each fighter on the field represents a source of damage and HP. Every carrier bay represents a source of regenerating HP. Carrier bays wear down during battle, starting out at high power and becoming fatigued as the battle drags on. However, more carrier bays solve the problem in a multiplicative fashion. Not only do you get more fighter replenishment in the form of direct production power, but you also gain less carrier fatigue because the stresses of lost fighters gets spread out more. It's much faster to replenish a fighter when the ship is at full strength, and a trickle of losses will maintain that strength to continue replacing fighters at max speed. The math can be seen in direct battle, where the best addition to a fighter heavy fleet is to stack on more fighters. I don't really understand the exact formula for how carrier fatigue works, though.
Once you start swarming the field with fighters, AoE weapons become vastly more powerful. Perhaps players should look into using more flak weapons? Weapons that hit multiple targets, weapons that chain across nearby targets and similar skills all punish swarm play. If they aren't up to the task of clearing out a swarm of fighters, then nothing really is.