The SFU version of Star Fleet was intended to be a unified navy, superseding the various planetary fleets during the course of its creation. There were certain political compromises during the course of integration, as various member planets kept "training squadrons" which were eventually formalised into the various National Guards.
(Indeed, the previous generation of unified Star Fleet ships were transferred to the National Guard fleets when the current crop of ships started to enter service back in the Y120s.)
Earth has had a disproportionate impact on the Federation, even in the SFU; the first tactical warp drive was pioneered at Earth, the primary fleet shipyard is in Earth orbit, and the only pre-unified ship class to survive the transition to the modern era is the Terran light cruiser. (The Fed police ship looks the same as the old Terran destroyer on the outside, but has a different internal configuration; whereas the CLs have been the same hull type throughout its long service history.)
The
Inter-Stellar Concordium had their own process of integration, too. Each of the pre-ISC planetary fleets (as shown in
SFB Modules Y2 and
Y3) have their own names and designs; while the standardized hulls of the unified ISC Navy and Police have a more "neutral" set of names. (In their case, the "two-prong" hulls which served the ISC in the Early Years were transferred to the Local Defence forces, the ISC equivalent to the Fed National Guard, when the modern three-prong ships entered service.) The early Concordium had a sustained effort to try and develop a balance between the five founding species, but it seems that the humanoid Veltressai have become the leaders of the ISC by the modern era.
The main issue with Fed "civil war" scenarios is that, while they are viable with the Early Years planetary fleets, there isn't a lot of technological variety between them. Since most of the major planets were already members of the Federation by the onset of tactical warp, most of their warp-refitted ships adopted the same types of phasers-2 and photons. Only the Vulcans and Andorians did things differently; the Vulcans were early adopters of phasers-1 and special sensors, while the Andorians went instead with a home-grown version of drones.
The pre-ISC fleets are different, in that their warp-driven planetary ships were built before the Concordium came into being. Since the five planets were still rivals back then, they each developed their own heavy weapons to mount on those ships. It was only when they first started to field unified hulls, a few decades after the ISC was founded, that they went fully into the process of combining their efforts into a new generation of weapon systems.
If we ever get into the Early Years in
ACtA:SF, the planetary fleets would be neat to see fleshed out. But even so, the early ISC might end up being a more fertile ground for inter-planetary conflict than the early UFP.
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