Yes, but the vast majority of base operations are not using any of the skills given by the naval career. Unless you assume everyone has access to advanced education, where you can at least have a chance of Admin.
I see no reason why you would not limit the hard admin to officers and specialist staff who are educated. You don't need the Admin skill to fill in forms you need it to circumvent bureaucracy. If you are the bureaucracy you just follow the tram lines. "Sorry Sir, I can't issue anything without the correct authorisation." and the time honoured "I don't care if you can see it on the shelf, the computer says we don't have any."
The Service/Crew skills are: Gun Combat x 2, Vacc Suit x 2, Mechanics x 2, Electronics, Athletics, Melee Combat, Pilot, Gunner, Flyer.
All the Intel, logistics, crew support, corpsmen (medics), and so on are Admin, Medic, Steward, or other skills not available or extremely limited access.
Many of those skills are available as background skills. Unlike adventurers most peoples day job consists of Routine tasks and they have the right tools for the job and much of it will be automated. If you need specialists then it tends to be an officer leading or you get a genuine specialist. Many corpsmen will be stretcher bearers.
Where is it written that naval ratings need Steward skill? They don't deal with high class passengers or nobles. Cooks will put things in the auto chef and the majority of their time will be refilling and operating machines. The rare time Steward in necessary you will get specialist training (as a result of Event 8) or they might draft in a Steward droid who will do a far better job of it.
The Imperial Navy Handbook p69 seems to disagree with you.
"Deck Personnel: Deck includes a number of nonspecialist personnel who carry out whatever tasks are required, typically general maintenance and security of the vessel, but Deck personnel can be loaned to other branches whenever needed. In addition, Deck includes a number of specialists including stewards and medical assistants."
That section also covers medical officers, chaplains, logisitcs officers, operations officers and the crew that support them. All are Line/Crew.
Traditionally the shipyard workers are not considered "line" (they are staff) and would probably be Engineering in Traveller's breakdown.
Most shipyard roles are logistics roles. The building and maintenance of ships will probably not be by Navy personnel (unless it is part of their training), that will be done by contractors. Most shipyard duties in my experience are logistics, movements and security. Some Engineering will be needed to conduct repairs to vessels (and these might be Navy personnel in forward bases). The specific equipment that need Engineering are called out in that skill, but the majority of repairs and maintenance use the Mechanic skill, one of the main skills of Line/Crew and Service. This might also be a punishment detail or a backwater posting for "difficult" personnel.
Some personnel might have had a near miss in their career (or got into a relationship) and switched to Line/Crew at a shore base as a softer option where they can spend weekends in a safer environment (possibly with their partner close by).
Who knows, maybe in the future all that is handled by government contractors and you don't have enlisted specialties in supply and crew support or perhaps "staff" specialties aren't distinguished from "line" specialties.
A lot depends on how space navies work. Star Trek has all the officers actually doing work instead of telling people to do work. Which is great for TV, but isn't how things work in surface navies. But games also rely heavily on fictional tropes that are familiar to the players, many of whom have never been anywhere near the real military. So you get lots of people who think "Sir" is the correct address for a Master Chief and that the Chief Engineering Officer is actually be the best wrench on the ship, rather than being the guy whose job is to know who the best wrench is and make sure they are on the most important task.
IRL, the helmsmen, navigators, engineers, etc on naval vessels are enlisted personnel with Surface Warfare/Line Officers supervising them (except on nuclear vessels like submarines where the engineering officer will have a lot more engineering training, but even then they aren't the best hands on engineer).
In my experience most maintenance is conducted in accordance with approved maintenance documents where procedures are clearly documented (i.e. you follow the recipe). Deviation from those procedures needs to be authorised by senior engineering officers. When you are at sea (in space) you may have more latitude and require more experienced people to make a judgement on the fly, and that is why ships have Engineers aboard. Ashore you need people who follow the procedures.
Anyway, the point is that Traveller's character generation is designed to create characters suitable for mid life crisis adventuring. So the skills (and the mustering out benefits) are targeted towards that.
The character generation mechanism was also supposed to be the way you generated NPCs. Everyone you met in traveller was expressed as <X> terms in <Service>. If you don't have that mid-life crisis you can stay in and what falls out is a "normal" navy career path. If you are angling to maximise your pension (a not uncommon driver later in life) and have already made Captain, Line/Crew is a safer option without sacrificing anything significant,
That's why 1/4 of the results for Service + Crew are personal combat skills and barely half are "job skills" (Vacc Suit, Mechanics, Electronics, Pilot, Gunner). And two of those job skills are actually for other branches (Gunner & Pilot) and only show up because the same service skills feed all three branches.
Flyer, not Pilot. Flyer covers Grav and that would be every piece of MHE in a shipyard, most shoreside movement roles and armoured vehicles. It could also cover air superiority fighters and patrol craft to protect a base. Combat skills could equally be there for guard duty and Gunner for ground defence batteries.
No one designed the rules to model society at large. You can obviously use it for that, but its going to give weird arse results. Just like having your village parish priest in fantasy worlds ends up being a warrior-mage because "Cleric" (a specifically adventuring class modelled on holy warriors) is the only game mechanic for priest in D&D.
You could expect the rules for a Navy career to reflect the Navy though. Ultimately it is your choice and you can read into it what you want. Your interpretation is not "wrong", but that doesn't mean mine is either.
We are not going to agree and we don't need to.