Figure that depending on the circumstances, electronic warfare (or in bigger engagements, the fog of war) would also be a big factor, potentially making it difficult for the capital ships to single out fighters and destroy them. Then again, in the latter half of WWII, Navy gunners were taught not to try and single out targets, instead simply filling the sky around the ship with overlapping fields of spray-and-pray with some liberal application of radar-assisted proximity-fused 5 inch shells.
Sometimes “Effective” has nothing to do with “Efficient.”
I’ve seen some settings where the fighters really can’t take down an enemy warship, barring some jarring weakness (like an exposed thermal exhaust port leading to the reactor core) or unusually skilled flying (the old Wing Commander standby of flying into another ship’s hangar bay to liberally lay down point-blank-range destruction before hopefully escaping again).
In the Honor Harrington books, they don’t have proper fighters, but they do have Light Attack Craft, which end up filling some of the same niches. They end up not being capable of destroying most major warships, but are plenty capable of using their superior acceleration and numbers to swarm the smaller picket and escort ships, giving them something considerably more pressing to worry about than screening incoming fire from the enemy fleet. Essentially, on their own, they are little better than patrol boats, only really being able to sound the alarm if an enemy force arrives. In larger numbers, they become team players, supporting each other and their own major warships.