Thank you for starting this thread.
As to your question about the "purpose" of the "primary hull"/saucer shape, I would suppose that, in-universe, starship designers and builders found the saucer shape to be useful and practical as a "habitat hull" concept, that is, a starship's primary purpose is going to be to house and carry a crew to distant destinations and the designers/builders apparently settled on the saucer shape as a practical (and, perhaps "warp dynamic" and/or planet-landable) means of fitting that primary habitat into the technical conventions of starship design.
In terms of Hollywood mentality, there was an interesting discussion about how Matt Jefferies arrived at the
"distinct shape" of the Enterprise recently in the TrekBBS Tech forum that you may find interesting.
If I understand where you're coming from correctly, this kind of philosophical approach is probably long overdue.
Prior to his death, Mr. Roddenberry promulgated an elaborate set of rules (some say he pulled said rules out of his posterior) for starship design. Among them were the number and orientation of the ship's warp nacelles. While those rules were clearly intended to "invalidate" the even-then-growing body of alternative starship designs (FJ's tri-nacelled Federation-class "dreadnought" starship among them), and have since been broken even by the studio (not to mention a backlash in fan-based designs), perhaps it is long overdue to step outside of the fan-based orthodoxy and re-examine ship design philosophy.
Take the notion of "dreadnought" design, for instance...
1: FJ unwittingly led a movement of fan-based design that has flowered families of tri-nacelled, super-sized-saucered, multi-dished, covered with phaser banks starships that all seem intended to be the "ultimate bad ass" inflated outgrowths of the Constitution-class. From my standpoint, the Constitution-class
is the dreadnought. The Federation supposedly doesn't believe in warships anyway.
2: The only dedicated class of Federation warships we ever saw was personified by
Sisko's prototype Defiant in DS9. (And maybe the
Prometheus in VOY.) Neither of these ships fit the uber-huge stereotype that FJ started. And Sisko's Defiant seemed to take the concept in the opposite direction by making the warship concept into a small destroyer-type unihull shape. So maybe instead of uber-fat, tri-nacelled battleships, a Federation in need to warships would turn to heavily armed and armored destroyers instead. Such mini-starships would supposedly be easier to build and maintain due to their simpler shape and relatively small size, and probably much easier to mothball or decommission.
3: After reviewing
Forbin's recent Themistocles kitbash thread in this forum, I began to wonder what a TOS-era prototype (or limited-production) battlecruiser would look like if you set aside the FJ "dreadnought" orthodoxy. Let's assume that one of the ships mentioned but unseen in TOS was in fact, not a Constitution-class starship but perhaps a rare battelcruiser/battleship instead. How 'bout the destroyed Intrepid in "The Immunity Syndrome"? Apparently a Vulcan-crewed ship of 400 souls, what would such a ship look like if we assume, for sake of argument, that she was not Connie? What if the Vulcans came up with a very different, unorthodox design? I'm not saying that Intrepid would have to look totally unfamiliar, like the
Suurrok-class Vulcan ship seen in ENT, but maybe taking the basic parts of Federation starships and applying them unconventionally.
Maybe the first thing we would do away with is the familiar saucer. Instead, let's make the "primary hull" a vaguely missile shape, very loosely based on the Suurok. Here's an idea: take the odd-shaped secondary hull from FJ's Federation-class, eliminate the aft dish and embed a small sphere on the tip instead. Now make the back of that hull the front of the ship. The nacelles would have to be re-oriented backwards, of course. Now, imagine this design with no saucer, no third nacelle, and we'll really set it apart by fattening the "primary hull" to make it even wider. the fatter aft tip (the front of FJ's Federation secondary hull) would have two shuttlecraft hangars instead of one. And there would be a third hangar-bay amidships from the belly.
This would make a Vulcan-designed, limited-production warship very different from what we've seen in fan circles. Conceptually, this battlecruiser design would be at least as powerful in combat as a Connie and yet not intended to be the ultimate kick-ass ship (at least, not more so than Sisko's Defiant in the DS9 era).
And to give our new battlecruiser a more combat-oriented look, we would orient the nacelles,
Phoenix-style, so the exposed parts would all be inboard, and we'd beef up the armor on the nacelles so they could take direct hits and still keep going.