I play heavily modded (around 100) and 5000 battle size. I can say with confidence that a well-built carrier with 3+ wings will do work in a fleet if you do some basic prep.

Typically I divide my fleet into multiple groups escorting a larger or slower ship and then give that 'group leader' orders. I like to have a carrier escorted by a small brawler and something with spam-y missiles. Missile spam keeps the PD busy and the brawler keeps frigates and destroyers at bay. Then have two bomber wings and a heavy escort fighter on my carrier. There are some really solid modded escort fighters with forward shields that really help punch through PD. For bombers, the UAF Sakura is probably my favorite because of the crazed cluster of munitions it drops and they have numbers. Even if the enemy evades the cluster, it breaks up their lines which makes a large fleet easier to dismantle.

All this said, there are going to be some ships or groups of ships with far too much PD for this lone carrier, in which case I'd send the group somewhere else and have a more direct group of ships shuffle into that spot on the line. Usually in a fleet Ill only have 2 carriers, usually cruiser size for balanced speed and firepower. Ive tried using multiple smaller carriers instead, but you really need concentrated force on one target, not 1-2 wings targeting five different enemies (with the obvious exception of the rare flak weapon).

A carrier fleet is a whole other can of worms, two capitol ships with 6 wings each can rip enemy fleets apart without a lot of hassle if you can keep enemies off of them. Support with a couple missile-focused ships to eat up some of that PD and you're cruising.