Is it any stretch to say that something like a Sobek or Deimos, which encompass substantially more volume, couldn't in turn hold substantially larger crews?
No, but the question is - what does that crew do?
A carrier like Nimitzs needs that much crew and we know why. Pilots usually fly in shifts - ergo a carrier would usually carry 2 if not 3 times more pilots than it has craft on board. Some of the craft are 2-seaters.
so for a Destroyer that normally carries 120-150 combat spacecraft, we have a MINIMUM of 300 pilots. Next we need flight crew...of which you again need quite a few to service the airplanes. and they also work in shifts.
All in all, just on aircraft you'd need A MINIMUM of 1000 people. Note that the Nimitz, with around 80 aircraft, has 2800 personnel listed as pilots and flight crew.
The basic ships crew is roughly 3000 people. For the Enterprise the numbers are 3215/2480. Kitty Hawk 2930/1782 Forrestal - 2900/2279
So a little less than half the ships crew is just there for the aircraft.
So assuming a similar distribution, roughly 4000 crew on a FS destroyer would be there just for the aircraft.
In comparison, crews for combat warships are drasticly smaller - 1500 for the Iowa battleship, which is almost as big as an aircraft carrier. Between 300-100 for other US ships, raging from cruisers to frigates and destroyers.
It leaves me to wonder what do the 6000 on the corvette actually do?
It only has 30 turrets or so, so there's not that much to mantain or control (Iowa has over 100).
So that leaves me to think wether that corvette was a good representative of the standard number. Maybe it was ferrying troops or scientists or refugees?
Given that a corvette is roughly twice the length of the Iowa (ergo, it has more than twice the volume) I can see it having more (around 3000).
But I just don't see what the 6000 would be doing.
And since we're at the matter of fleet numbers, knowing the number of people in the fleet and the number of people on the biggest ship, it's not a stretch to be able to come up with a reasonable fleet estimate. Simple logic dictates that there are more cruisers than corvettes in a fleet and more destroyers than corvettes.
A fleet is highly unlikely to have more than 2 destroyers, given how important they are and how costly and big.