Please note part of this is speculation, but the original quotes leave some room for interpretation and I guess the writers didn't have any specifics in mind.
From The Savage Curtain:
Scotty, inform Starfleet Command. Disengage nacelles, Jettison if possible.
"Disengage" and "jettison" are rather broad. While it might suggest dropping the names, it might also refer to simply jettisoning fuel like real world planes might do in emergencies.
The quote from The Apple is way more specific:
Discard the warp drive nacelles if you have to, and crack out of there with the main section, but get that ship out of there!
The writers probably intended this to definitely be some mechanism to get rid of the "dangerous bits" in some kind of fashion and to build tension, but ultimately it wasn't picked up again and most likely retconned.
What brings me to this conclusion two big features specifically introduced with the main protagonist ships in both The Next Generation and Voyager:
- The Galaxy class (i.e. Enterprise D) introduced the saucer separation as a big thing, which is also why it's heavily featured in the pilot episode. It's quickly forgotten again for most of the episodes, but it never sounded like a stock feature common on other ships, especially considering it would have been way more useful on many episodes.
- The Intrepid class (i.e. Voyager) added jettisoning the warp core as something new (mostly to add the prospect of "never getting home" as an undesired plot outcome other than losing the whole ship) after TNG promoted it to possibly the most likely cause of ships getting destroyed.
If either of these two features (in any kind of iteration) would have been available since Kirk's generation, wouldn't it have seen more widespread use during and after TNG?
As for your model kit: Losing one or more nacelles during battle wasn't a too uncommon sight throughout the series, when they wanted to depict a damaged or derelict ship for plot reasons. Maybe the creators simply wanted to provide an easy way for this without breaking the actual model?