There is no need for such a thing as "holding the ground", what ground are we talking about when you are introduced in an universe where you can be here or there in a fraction of a second?
Holding ground is inviting the enemy to crush you, that's why fighters got their jump drives, that's why destroyers have their jump drives, so you can run.
It seems more plausible to have a destroyer that can jump further and faster than one that can stand its ground alone.
The destroyer leaving the area would not interfere with the deployment and retrieval of fighters.
Since you fail to understand my metaphor, allow me to expand upon it.
Flight ops depend on a base. The fighters and bombers depend on a base. And when that base can
move, it causes problems as anyone with even a rudimentary grounding in the history carrier aviation would know.
Point Option, where you return to, moves in an unanticipated way. This, at the very least, must be communicated to fightercraft in flight so they know where to return to; this takes time and also introduces some risk. Similarly while a ship is in transit, and for some period of time after exiting subspace, it will not be able to recover fightercraft. If you have to run away from every Lilth, then the Shivans can easily keep you hopping using only three or so. (And recall the Shivans likely can afford to do this.) Your Hecate is now useless.
A destroyer, if threatened by an enemy ship that isn't at least its equivalent, needs to be able to kill that ship and continue the mission without interruption. Ideally, it should also be able to kill something roughly equivalent as well in conjunction with its escorting fighters. The Hecate does not do either.
What's the alternative to a carrier?
The existing destroyer, as embodied by the Hapshepsut, Orion, and Typhon. Able to carry a significant number of fightercraft and yet capably defend itself against hostile cruisers and corvettes.
Everyone always talks about surprise attacks, but how are you going to surprise them in the first place? First you have to find them, second you have to make sure they don't know youve found them, and third you have to hope they don't move between you finding them and your forces launching an attack.
Simple recon. We're fighting the Shivans, remember, we don't really know what they can do, but we do know they can probably blanket the system in fighters for recon duty if they have to. And they demonstrated an ability to locate targets regardless of whatever countermeasures were taken in the Great War, considering you were forced to escort ships carrying top-secret projects delving into antimatter weaponry that would have been well-hidden.
If it gets ambushed it can either launch more bombers, fight back with its BGreen, launch some more fighters, call for reinforcements, or bug out all together.
The reason why carriers of some kind or another are needed is because fighters and bombers operating in system must have a place to re-fuel and re-arm. Moving to another system takes a lot more time.
Bombers take time (and thereby expose the ship to damage), and take up space on the flight deck that isn't being used for more pressing concerns, are not guaranteed since bombs may be intercepted, and could also be used to contribute to more offensively substantive strikes. The best weapon for destroying incoming fightercraft is a fighter, but the best weapon for attacking capitals remains the beam cannon. An Orion is better-equipped to handle a variety of threats than a Hecate. It's already placed its faith in escorting fighters for defense against hostile fightercraft, as it should, and it has an array of beam cannon for dealing with errant cruisers and corvettes.
I'm not arguing against carrying fighters; I'm saying that the nature of FS combat means that a purely or even mostly carrier design is a misstep. The hybrid presented by a Hapshepsut- or Orion-like ship (or for that matter a Titan or Raynor) represents a more effective and efficient tool.