Sorry, but I can't buy that the Kelvin was 1500 metres long. I like to think that the Kelvin also existed in the prime universe, and if it was that big it would make the original USS Enterprise look tiny in comparison. I find the idea of vessels that gigantic existing that early in the original timeline VERY hard to swallow.
I think it's very possible. Starfleet ships built after the Kelvin could have shrunk in the prime universe based on more automation. The Kelvin, being an older ship, probally had a crew of cooks, laundry staff, plumbers, and other janitorial and upkeep staff. Probally more crewman in engineering too, the bridge itself seemed quite crowded. Then as more systems of that nature become automated, with replicators and perhaps more mechanical devices, sonic showers... less plumbing, less mess hall staff, smaller crew smaller ships, and that leads to an Enterprise seen in TOS.
Then maybe after an attack by a ship as big and powerful as the Narada arrives on the scene at the point in time that it did, it may of changed the mindset of starship designers. More automation, but also more power, better weaponry, bigger warp drives, , they got to Vulcan pretty damn fast, I say these post-Narada Starfleet vessels are big heavy power pigs because the Narada changed the game. Technology in ship building advanced at a quicker level. The universe became a bit meaner and chaotic than perhaps it was in TOS's time. So, Starfleet and their ships adjusted accordingly.
Ding, ding, I think we have a winner. To me that makes the most sense. For perspective, if a WWII era Lexington class aircraft carrier can be 888 ft (271 m) long and have a complement of 2,122 I can believe a 23rd century starship would be able to have 800 people on board. Needing more support personnel than the TOS Enterprise because of it being older and having less automation and supplies makes sense to me.