It still seems more than a tad on the low side, although I can't marshall more than a gut response based on "space is BIG, also 3-D in volume, not merely acreage".
I covered that in the first couple of chapters. In the first place, it isn't "space" that you're exploring, it's the various things IN space. Solar systems, planets, asteroids, comets. Gravity tends to pull those things into little knots that aren't too expansive in themselves, but the space BETWEEN them is incomprehensibly vast.
For a given cluster of stars (say, 8 or 9 systems gravitationally bound) a single starship could explore the entire cluster over the course of a year, bouncing from one system to the next at a modest warp 3 or 4. For that entire year it might be the only starship in that cluster, or indeed, the only starship within a dozen light years in any direction. Other more "lively" areas along known trade routes or in the vicinity of populated colonies would get a stronger presence, but even that would be a ratio of perhaps one starship per solar system, IF that.
This doesn't change all that much even in the 24th century; the Federation simply controls a lot more systems and planets and the fleet is expanded accordingly.
Also, there's the issue of logistics. However many capital ships you've got in active service on defensive, peacekeeping, research and exploration duties (and that last is what's really going to complicate the picture in a way our present-day navies can only begin to imagine since it's been a century or two since the last bit of ocean was properly mapped), you've got to keep the support network behind them firmly in place.
A "network" would imply sharing of resources from a single point, distributing it out to its end users on the frontier. That is decidedly NOT how Starfleet does things, nor could they afford to with the distances involved.
Fleet support comes primarily from the Starbases, which in turn depend on the colonies and civilian population centers built around them. The starbases keep the fleet stocked and supported using materials, food and fuel produced locally; very little gets shipped out to Starbases from Earth, although quite a bit gets exported from the colonies TO Earth.
The reason for this is twofold. First, it makes a lot more sense economically to rely on the local industry to support the fleet, as that strengthens the colonies' own local economy (giving everyone something productive to do). Second, relying on local resources shortens the supply chains dramatically and allows each starbase and its adjacent colonies to act in "Standalone" mode in the event of war. So a war with, say, the Klingon Empire wouldn't necessarily involve a situation where the Klingons start raiding Federation shipping between Earth and the Frontier, because most of that shipping is civilian in nature and has very little strategic value. Instead, the Klingons would have to try and take the entire colony: the dilithium mines, the metal works, the factories, the farms, the hospitals, the labs, the motor pools, the dry docks, the shipyards, the power plants, the pubs, the stadiums, the schools, the local militia. The whole kit and caboodle. The orbiting starbase and its ground facilities would almost be their own pocket Starfleet and could still operate independently (for the most part) even if the entire rest of the Federation had burned to the ground.
What little shipping and support DOES take place is handled by robot freighters (the Woden et al) or by the Earth Cargo Service aka the "Merchant Marine" mentioned in TOS. There's also the civilian privateer freighters unaffiliated with any government service, from various Federation races, who would be happy to take a high-paying commission from Starfleet on the rare occasion they need something they can't manufacture themselves.