Name something small ships could do better.
Sneak attacks, precision attacks, multi-directional attacks, close range combat.
No such thing, why can't big ships do that, why can't drones/missiles/etc do that, why can't everything do that.
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One large ship versus its mass and cost in small attack craft will need to be a smooth adamantium sphere if it wants to not have its engines blown off, its access hatches and shuttle hangars gouged out, and every nook and cranny not protected by copious point defense crammed with sabotage-happy little ships.
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Wrong. A large ship can have a hell of a lot more armor than a small ship can have weapons.
Moreover, if this is somehow true, why not cut the cost even more by replacing the fighters with drones?
Consider the case of two ships versus a ship and a fighter swarm. Unless one of the pair of ships is a dedicated point-defense ship, things will go rather badly for the two. With a fighter escort, the single ship can have its entire weapons complement focused on killing other ships.
If missiles or other projectile weapons are things, a ship without good PD is pretty damn dumb.
If there are only energy weapons, there is no way the fighters have strong enough power sources to power weapons that can go through armor.
Assume that the pair is a PD ship and a mirror ship of the other one. In a long range engagement, the fighter-side ship-killer can destroy the PD ship...
Actually, the dedicated ship-killing non-PD ship would logically be better at killing ships than the carrier, since it doesn't need to have a bunch of space and cost taken up by hangars, fuel storage, and the like for fighters, so the carrier would be blown up. Unless these "fighters" are somehow self-sustaining interplanetary craft, which...kind of makes them less and less like fighters.
Hence, the carrier-battleship would be destroyed by the dedicated battleship before the PD ship would be destroyed. Especially if the weapons in question were kinetic and not energetic in nature.
If both ships are a mix of PD and ship-killer,
And why the hell wouldn't they be?
So no, especially considering the tech level in ER, a fighter swarm can be advantageous.
Considering that your entire argument is full of holes, and that
every argument for them applies even more strongly to unmanned drones, missile-like combots, and the like...no, there isn't.
PD weapons would either be numerous enough to engage the whole swarm - which means they'd have to be small enough to fit on fighters themselves
I don't get the logic behind this or how it would be in any way relevant, since the PD guns would only need to get through the relatively thin armor of the fighters rather than the thicker armor plating of the large ships.
- or large enough to outrange fighters, in which case they'd draw power away from the ship's main guns.
Considering that the sole requirement for "powerful enough to outrange fighters" is "stronger than the fighters' weapons," no they wouldn't. Especially if they included a kinetic component.
It's quite possible to build a strategy on this as well,
Ah, but would it be effective against anything except your hypothetical fleet of ships incapable of dealing with carriers or fighters?
Anything precise enough to target a fighter over two hundred thousand kilometers away would be relatively fragile, and a ship on the other side could just as easily use a similar weapon to take out the point-defense weapon.
Why not just use the weapons, then?
Even if it's a smaller target, nominally, it's situated on a large and far slower moving ship.
Now the carriers are smaller and faster than the other ships?
Bottom line, it's far too early to discount space fighters completely. Fighters and shuttlecraft have uses besides combat, and their combat uses depend largely on the tech level and the strategies you're employing.
It's very, very setting-dependent, and the harder the setting the harder it is to justify space fighters.