It's not an issue of industrial output. It's an issue of technology. XIV ships are tweaked to perfection and the fact that they don't break in spite of having top tier armor more flexible systems (more ordinance points) is only achievable thanks to the fact that they were made using the best possible available technology in the Domain. Technology that was probably far more precise and required very different materials to what we have now in the Persean Sector
Chicomoztoc is large, but it is also a wasteland. Compared to old worlds of the Domain it has nothing. It is using a nanoforge, sure. It has functional industries, sure. It has military patrols guarding it, yes. It probably has humongous metropolitan cities sprawling across tens of miles of its land.
But that doesn't mean anything. The level of technology in Starsector exists between being relatively comprehensive to magical in nature. And the thing is that XIV is meant to be more latter than former.
Tessies could easily assemble XIV ships. Remnants could probably figure that out too. Tri-Tachyon would be able to if they cooperated with Hegemony rather than jumped at each other's throats. But that is the point of the game. The world did not die because it disconnected from the core, but because no one bothered to build anything on something else than military-industrial prowess.
I feel like you're making a lot of assumptions here -- which admittedly, is kind of the point - a lot of Starsector lore is vague and all we have in some areas is speculation - but it's still worth noting that your assumption that the Hegemony doesn't have the technological capacity to build more is precisely that: an assumption. I'm not trying to be dismissive of what you have to say, of course, but I feel like asserting that the XIV hulls are impossible to manufacture for some unknown technological reason is premature.
You're also being unfair to Chicomoztoc: yeah it's a wasteland, but So What? It might be unremarkable compared to the Domain-typical worlds, but the raw human strength of hundreds of millions of people is not to be discounted. Its heavy industry is suggested to be immense: it's a whole order of magnitude larger than Kazeron, its closest rival in industrial strength (and Kazeron is only a
rival because of its pristine nanoforge, which Chico also has). To say the demography of Chicomoztoc "dominates" the Persean Sector almost feels like an
understatement.
A strong industrial base is necessary for technological developments. To acquire a technology, a society needs industry and talent. This is a setting where the Ziggurat exists, mind you -- obviously, TriTach specialises in advanced tech research, but the Hegemony still (as seen by the seizure of Kallichore and Daud's 'new terms' over the campaign) exercises practicable suzerainty over the Galatia Academy, which produces some of the Sector's finest minds -- many of whom will become top-level Hegemony theorists, officers, engineers, scientists, etc. The Hegemony, on top of this, has access to existing XIV-type hulls and presumably has, or can acquire, full knowledge on how the structural modifications fundamentally work.
I still see absolutely no reason that the Hegemony would be incapable of manufacturing an existing XIV hull. XIV ships aren't 'magic' -- they have better armour and a more solid flux grid.
One thing some people automatically assume here is that Hegemony actually seeks to produce them, it might not be the case. There is nothing really exceptional about XIV variants, the modifications they have, as per 14th Battlegroup hullmod description, are just 100 "standard units" increase in armor plating and 4% improved capacitors performance. This is something that can be easily reproduced with existing hullmods, and while this seems to be the kind of meticulous optimisation Domain era engineers cared about, its probably not a priority anymore.
To be clear, armour doesn't scale linearly -- 100 units can actually be a huge increase depending on what it's mounted on, and it's still good on less armoured hulls.
But yeah, I'm not claiming that the Hegemony
wants to manufacture more. Just that they have the capacity to. Obviously, it's suboptimal military-economic strategy to produce these very expensive hulls when Hegemony warfleets come in industrial ol' reliable bulk, not seamlessly well-fashioned ships.
The vibes I get are definitely that they don't produce
more, and I think Occam's Razor suggests the "too expensive" rationale checks out. There's also probably a vested interest for those annoying Eventider aristocrat slimeballs who want to maintain their political status as descendants of the 14th. Imagine the horror if Baikal 'Hive-Dirt' Daud could produce XIV hulls for his low-life Mozzie criminal friends!
And there we find the anachronisms at the Hegemony's heart: the Domain is dead, these venerable old warships are all that's left, and in part they represent perfectly the reasons that it died. Despite this, the Hegemony cherishes the mythos of the 14th Battlegroup, playing inside the gargantuan skeleton of the civilisation it helped kill.