There always appears to be plenty of space until one looks at the various decks in latteral crossections. Then you discover how little space there really is inside this hull.
If you add a reasonable hull thickness plus internal structure, then there is even less room. We don't know exactly how thick the hull was meant to be but there are clues. First, there is the portion of casing visible over the Hangar Deck doors, which works out to be about 26 inches in thickness. Next are the known displays of the ships ability to sustain all manner of high structural loads, up to and including the nearby detonation of a nuclear device.
I don't know how thick the hull would have to be to withstand such loading (we also have no idea what the hull is made of either) but in addition to structural loads, it must also be hardened against other types of threats to the lives of the crew. First and foremost of these protections would be against radiation (this is probably the top threat for crews in space), next would be thermal protection followed by magnetic and finally electrical. I imagine that these considerations would result in a layered hull of varying thicknesses resulting in a fairly deep total thickness. There might be layers for protection from other less obvious types of threats as well.
Before anyone jumps in with comments about how these issues would be dealt with by "force fields", keep in mind that Starfleet architects would be well aware of the many instances in the service histories where electrically driven systems were denied or rendered inoperative, thus leaving the given crew with only the capabilities of the basic ships structure to protect them. This would be the final fall-back survival position for the crew and as such, the ship designers would be obligated to give them the best survival chances possible. In fact, we know that they did so by virtue of the many extreme life threatening situations the ships have survived.
I see this design approach as being similar to that of a battleship. On a battleship the crew have heavy long-range guns, medium-range guns, and close-in guns to protect from threats of various levels of immediacy. They also have torpedoes and ECM capabilities for even more protection but for the most part, these systems all rely (to different degrees) upon a functional ships infrastructure, mostly its electrical generating capability. Take that system away and the ship becomes a "target", its only protection then being the passive ones, namely the armored hull.
This "last ditch" capability would be present on our "Starship" as well, in the form of a thick outer hull with heavy internal bracing. Though we never saw the true hull thickness (and it might well vary from section to section, it does not necessarily have to be uniform), we always saw the heavy internal structure, in nearly every set.
These are few more things to consider when creating an inboard profile or deck plans.