In war time, ship production would likely jump through the roof.
Yet it doesn't appear to do so - we see no explicitly new ships in the Dominion war, save for Sisko's second Defiant
. Older designs remain prevalent, and only registries lower than those of famous prewar ships are ever observed.
Plus, Starfleet is dangerously short on ships in peacetime. Why would this be, if Starfleet were capable of building more ships? It's quite possible that ship production has already hit the roof in peacetime, and further ramping up is impossible.
We know canonically from WHMHGB (TOS) that ships can and have traveled all the way out to the galactic rim, and have explored all the way inward to the Great Barrier around the galactic core.
Since both the outer rim and the inner barrier are imaginary characteristics of the Trek universe rather than real physical phenomena, we don't necessarily have to assume that they would be quite as distant as the real (if ambiguous) outer rim of the Milky Way disk or the real galactic core.
But let's assume the TOS voyages indeed went tens of thousands of lightyears outward and inward along the galactic plane. A hundred such sorties would still only chart an insignificant volume of space. The exploratory routes would be mere thin lines, no thicker than the maximum range of starship active sensors (the TNG Tech Manual suggests a few dozen lightyears at most) in a vast volume that remained unexplored despite the voyages. It wouldn't be until tens of thousands of radial sorties were made that their volumes would begin to overlap at the 8,000 ly range.
Apparently, Starfleet doesn't support much of a presence, as it takes months or years to investigate the mysterious cessation of communications from a million-strong colony or a starship on an important assignment. And there isn't any sort of a credible perimeter defense, as encounters with unknowns and hostiles deep within UFP or UFP-explored space are not considered surprising at all.