My problem is the TNG aesthetic set up an expectation which was never again adhered to, specifically with the bridge.
The idea behind the design of the bridge was that Starfleet in the 24th century was so advanced that many of the ship functions were automated. Leaving aside the fact that such a level of automation clashes with the 1000+ crew (if automated, why do you need so many people?), later shows and ships attempted to portray themselves as more advanced by having more bridge consoles. However, more consoles should equal less automation which should equal less advanced by the TNG formula.
We don't how much automation is going on, however. The TOS was the size of a modern day aircraft carrier, and those ships usually carry thousands of crew, compared to the ~430 of the TOS-Enterprise. The D is several times larger, with much more volume, but still far fewer crew than today's carriers.
As well, TNG never really went in depth about crew functions, but we do know that there was plenty of work allocated to non-ship operations, such as research, diplomacy, and medicine. The D being a hybrid ship and mission of science and exploration could mean more crew devoted to those duties than ship operations.
Carriers have such huge crews because it takes a lot of folks to run a floating airport. Modern cruisers and destroyers have crews of 300-400, which is probably a better comparison.
For Kirk's five-year mission Enterprise that might mean 230 (using Pike's crew size) needed to run the ship and 200 mission specialists/scientists (maybe some of that number is additional security support).
We can postulate using a similar amount to run the much larger Ent-D with greater automation, leaving around 500 mission specialists/scientists/diplomatic corps with 250 family members to get to the 1000 number.
Modern cruisers and destroyers aren't closer to the TOS-E in size. Plus, the fact that much of a carrier's crew is devoted to other operations is sort of my secondary point, and so it's probably true for the E-D as well.
Overall, what I'm getting at is that 1000 people on a ship sounds like a lot, but for a vessel the size of a Galaxy-class, it's probably pretty spacious in there and isn't a sign that the E-D is gasping for automation. (indeed, any given time we see the E-D's corridors, it doesn't have nearly as much traffic as the TOS-E's corridors)