The Hecate was designed to counter the Shivan fighter/bomber threat and to deliver the most powerful weapons in the GTVA arsenal: Bombs. Harbingers and the like. THESE are what took down most of the Shivan capital ships in the Great War, including the Lucifer itself. It makes sense that they would design a ship specifically to perform such tasks, and that is the Hecate.
Carriers are good for power projection IMHO. Easier to patrol and respond to many small things - a perfect vessel for hunting down pirates and generally policing systems.
It also helps that if a bunch of fighters getting killed trying to take down an enemy destroyer, than the losses in personal and material is much, MUCH less than if a beam cannon toting Hatty gets blown to hell in the same engagement. It's very similar to the change in navel tactics during WWII, from big gun battleships, that could certainly rip through any carrier they ran into, to the carrier, which never even had to get remotely close. Battleships were too vulnerable to the cheap fighters, and so they disappeared.
Subsapce drives. Charge time. Important elements that need to be taken into account.
The carrier offensive power lies in it's bombers.
Bombers take time to launch, to reach their target and lock on, bombs have travel time and can be shot down. Beams have none of those issues.
Consider a battleship ambushing a carrier - the moment it jumps in, it opens beam fire. The Hecate will be hit by at least one full salvo before it can jump out.
In 30 seconds the carrier will receive the full brunt of the battleships power...in that same time, most bombers wouldn't even have target lock - heck, most wouldn't even be in range to being targeting. The carrier is forced to flee damaged (and thus is effectively removed from a fight), if not destroyed....and since the carier used it's jump drives last, the battlesip drives will re-charge first, allowing it to persue again (unless the carrier jumped to a friendly base).
The battleship can retreat as soon as it's jump drives charge again, and the carrier defense wings already "in air" will hardly be able to destroy it in 1 minute. Especially since it would mostly be fighters.
Next, consider a carrier ambushing a battleship. A carrier would launch fighters/bombers and send them after a battleship, staying out of the fight itself. The bombers would have to disable the battleship within 30 seconds to 1 minute MAX or else it will jump out...and if the battleship got the carriers location, we now have the above scenario. If not, it will run away to some safer location (either out of hte system, or in n asteroid belt, or a friendly base)