The fun thing is, we don't really have much reason to think that TNG era starships use wires of any sort in the first place!
The last time we actually saw macroscopic wiring in use aboard a starship was on the 2280s-vintage (but presumably oft-refitted) USS Hathaway in "Peak Performance". For all we know, ships from the 2360s are utterly wireless, for transfer of data, power, and transporter matter streams alike.
Those famed "plasma conduits" could carry all of the above and more, and be trivially simple to lay, as in "Phantasms" et al. they appear to feature as much intricacy as plastic plumbing today...
That aside, it's remarkable that we have basically never witnessed starship construction of any sort. It's always refitting, or test-sailing an already completed ship, or repairing existing vessels. Indeed, our only proper example of starship construction prior to ENT or the first reboot movie was from the Mirror Universe, where a Defiant class vessel was put together in primitive conditions in what appeared to be mere weeks.
Admittedly, a Defiant is small, but she's still as large as a Miranda by all appearances. If she requires weeks, a Sovereign might take months - but not years.
An interesting side note here is that we never saw any evidence of newbuild ships in the Dominion War, save again for a single Defiant class vessel. All other starships seen fighting sported registries lower than those of the DS9 and VOY hero ships, and their designs predated the war (or were kitbashes from components significantly predating the war, FWIW). If Starfleet doesn't manage (doesn't choose?) to build any ships during this crucial multi-year conflict, should this be taken as proof that it's impossible to build starships in any time shorter than decades, and an interstellar empire engaging in a war thus shouldn't even try? That is, unless they are betting on a decades-long conflict, which may be too pessimistic a policy for anybody to accept.
Timo Saloniemi