While all of the above is true, it seems expensive to have a carrier dedicated to this mission. Also, while the carrier has hoped out it is no longer on station to follow it's mission.
I think the fighters from "dirt-side" could be rotating on station at any given time. Also, for pirate suppression, how many are needed? A whole carrier compliment?
I use a "fighter tender". Without taking an historic earth WWII analogy to far, think PT boats (fighters) and a PT boat tender (often an LST). My thoughts are that this is cheaper, ties up less vessels and tonnage, and serves a similar purpose.
As for repair, a fighter transport could deliver anything from spare parts to new fighters on a run scheduled to take breakdown into consideration.
(I've read the "use a free/far/fat trader's cargo bay as a carrier for fighters" but, at one launch or recovery every 20 minute turn seems totally unworkable. IF you could even do it!)
Lacking a launch tube or configuration that permits rapid launch, the auxiliary carrier is for all intents and purposes a tender. Calling it a carrier is a bit of polite exaggeration; if I were the crew on such a ship, I'd be happier swapping tales about my time on an auxiliary carrier during the war, rather than explaining that I was on a merchantman drafted to act as a motel for little patrol fighters. It might make it a bit easier for me to swallow the fact that my ship was drafted by the Navy and put in harm's way to protect some remote settlement of little worth. However, that's semantics - anyone's free to call it whatever suits their purpose.
Recall the prime reasons a navy will draft merchants into the combat auxiliary role: 1) it's cheaper, 2) it's faster (i.e. faster to draft and deploy a merchantman than to build and deploy a ship specific to the mission), 3) current circumstances make cheaper and faster a high priority. The fighters are the core of this concept, and they aren't designed to be killers - they're designed to be cheap, small and hard to kill. Thus, the lack of a launch tube in a ship that only carries 6 or 12 fighters in the first place is not a major handicap: the ones on station can hold their own until the reserve group arrives to reinforce them.
The intended "recipients" of an auxiliary are out-of-the-way low-pop worlds with little or nothing in the way of a starport, the kind that might see one or two ships a month. These (IMTU) are too small to warrant the services even of an Imperial destroyer-escort - or a Zhodani destroyer escort, most likely. However, one likely strategy in war would be to field cheap little privateers to harass such worlds and hopefully draw off Imperial combat assets. Worlds with more appreciable starports would have their own fighters, customs craft and patrol ships to deal with such threats. It's the more remote worlds that don't have such assets where these auxiliaries would be stationed, and in that respect the auxiliaries would function as much as transports as anything else, delivering the needed fighters then hanging around in case anything happens to the fighters and, in the course of that, serving as an orbital base for the fighters so they don't have to start from the surface. The auxiliaries would have the parts and equipment for minor repairs and maintenance as well, something those remote worlds are likely to lack.
The intended opponents of such auxiliaries are ships like the 400 dT Corsair and privateering merchantmen. Such ships would find the agile little fighter hard to hit and, with its armor, harder to kill. For this purpose I envision a 10 dT heavily armored 6G Imperial fighter with a minimal computer; I call it Armadillo. With the small computer, it has difficulty hitting targets, but it's very hard to hit and even harder for a civilian-based privateer to damage, which makes it an ideal escort for a merchant to hide behind. Being such a difficult target, it has no problem fighting until reinforcements arrive, at which point numbers offset the difficulty hitting and the opponent (who is not armored) is best advised to leave.
The little fighters can survive against Zhodani DEs, though not for long and with no hope of doing harm. However, statistically they survive long enough, consistently enough, for their reinforcements to arrive and the escorted merchant to make it to the desired destination, which is about as much as one can expect from such a duel.
The intended role of such auxiliaries is, through their fighters, to serve as escort and orbital sentinel: persuading privateers not to be lingering in orbital space waiting for prey to show up, escorting outbound ships to jump, intercepting inbound shipping to make sure there are no unwanted surprises for the port below (like a hidden squad of raiding troopers), and escorting inbound ships against the potential sudden appearance of privateers. If they found themselves up against that Zho DE, their mission would be to ensure some jump-capable ship made it to jump point to go alert the Imperial Navy of the presence of an enemy warship; the ship carrying the message might well be the carrier herself.
And, as you point out, fighters can operate from planetside if need be, so the carrier can leave whatever undamaged fighters it has behind while it transports fighters for major repairs or goes to get more fighters. As to expense: an auxiliary carrier is a draftee. Subsidized merchant contracts permit the merchants to be drafted into Imperial use in wartime, and the nature of the worlds served by subsidized merchants can mean that the newly drafted auxiliary carrier may find himself protecting a world he is familiar with.
Free-trader-based auxiliaries would be a different story - there's need to modify the ship to have arrangements to accept fighter-sized craft into its cargo bay and to launch them from that bay. However, free traders are ubiquitous and cheap: buying up and refurbishing a 40-year-old retiree would be only a fraction of the cost of a new-built trader - and the stock free trader brand new is only a fraction of the cost of a purpose-built carrier of similar size. However, that's an option more likely to be seen if there aren't enough subbies to draft.
The auxiliary is a wartime ship, expanding the capabilities of the Navy in wartime (or in some immediate local situation warranting such measures) and then going back to peacetime merchanting in the long intervals between wars.
