They don't have unlimited power for heat and oxygen, and whatever else huge chasms would cause to drain
Compared to things like beaming stuff around, power requirements for heat and oxygen should be trivial, from TNG "The Ensigns of Command" we know that the Ent-D can carry at least 15,000 people
in addition to its crew of > 1,000.
the Enterprise from TNG, which was the largest hero ship prior to 2009
It still is. Shorter doesn't mean smaller, there's more than just length. A Galaxy class starship (GCS) is a lot wider (seconadry hull too), and a great deal of the Kelvinprise's 725 metres comes from the nacelles alone. You could easily get the same or more length for a GCS by simply moving its nacelles backwards, hell, you could go one step further by additionally rotating the saucer by 90° to achieve something beyond 800 or 900 m without actually adding anything to the ship!
If this is reliable, a GCS has 5.8 million cubic metres.
http://www.st-v-sw.net/STSWvolumetrics.html
I would estimate the Kelvin-1701's volume at something like 3 to 3.5 million cubic metres which would make its size comparable to an ambassador, smaller than a GCS or nebula.
But perhaps somebody has better numbers or actual calcs.
But besides that, the ship is just incomprehensibly large. It's almost on the star wars scale(which is limitless).
Not really. Does Star Trek generally have a scale limit? Whale Probe, V'ger, Yonada, Dyson sphere... If life forms count, there are also planet-sized space amoebae.
So I'd say no.
I seriously don't understand what all the fuss is about considering how ship sizes are handled in the ST universe. First of all, people pretend that the bigger the better the more advanced, more powerful which is just nonsense with tons of counter evidence. Look at those tiny Species 8472 bioships that make short work of giant Borg Cubes. Look at the Dominion which greatly relies on small attack vessels. Look at the Defiant. Look at those huge (hundreds of millions of cubic metres), "primitive" Kazon/ Trabe Predators. The Yonada is an asteroid converted into a ship with a diameter of over 320 kilometres, built by an even more primitive people etc.
Besides, it seems nobody gives a damn about 22nd century Vulcan cruisers with an estimated length of 600 m.
The NX-01 is supposed to be 225 m long.
I kind of appriciate the size of the alternate 1701 version(s) because it makes more sense to me. In both realities it was designed to operate for years on its own, regarding all those hostile Aliens, entities, and deadly anomalies, this seems more reasonable...
than something like this (original Ent-A).
Further, you can evacuate more people in case of emergency.