No mention is made of a "sustainer" engine, nor is there any indication the saucer section is equipped with such a thing.
Both in the TNG Writer's Guide and the Technical Manual.
Not for "Brothers" and certainly not in the tech manual. For photon torpedoes, yes, but I recall no reference to any type of "sustainer" engine for the saucer section.
I seem to recall it being mentioned somewhere in dialog as well
You recall incorrectly.
This is correct, it was never mentioned in dialog.
In the TNG Tech Manual, there is SOMETHING mentioned... but it's not described as a "sustainer coil." What's described is EXACTLY what I've talked about in the past - a "subspace field generator" which permits the impulse drive to accelerate the ship far more effectively than it could without the use of such a system (by reducing the "apparent mass" of the ship and the "apparent exit velocity" of the propulsive exhaust).
And while I believe that there
may be some "off-screen" mention of this being used to sustain a "handed off" subspace field (in the TNG Tech Man, the writer's guide, or both), there is no on-screen mention of the same.
Even the writers of the Tech Man made it clear in the preface that none of what they were writing was "gospel" and could be changed at any time if the needs of storytelling required it. (As clearly happened repeatedly.)
The argument we're having here is just inane. Vance is stating, categorically, that it is IMPOSSIBLE for a "subspace field" to do anything other than immediately collapse after cessation of delivery of power. Unless there is a specific quote someplace in the course of the series which states "it is impossible for a subspace field to continue to exist for even a moment after cessation of delivery of power" then the entire "argument" is based upon MAKE-BELIEVE INTERPRETATIONS of MAKE-BELIEVE TECHNOLOGY with no real, factual basis other than MAKE-BELIEVE SCIENCE.
I'm saying that there may be some reason, in some sources, to conclude something like that, but that there are other reasons, from other equally valid sources, to conclude otherwise.
I'm certain that several episodes of TNG showed the ship losing power and reverting to real-space after a finite length of time... ie, not the "t=0" instant that power was cut off. I can't comment on Voyager, because I couldn't make myself watch that show more than a handful of times. In DS9, I think we may have seen some evidence of both "takes" but none were ever really driving factors behind the storytelling (as happened several times in TNG) so I dont' recall offhand.
But.. it's ALL JUST STORYTELLING MAGIC, and the "magic" changed whenever the storytelling demanded that it do so.
However, if you want to talk about "what if Treknology were real," which is why we're all in this forum (even though we all OUGHT to realize it's all just "make believe"), you have to look at real-science parallels to things we've seen in Trek.
From that standpoint, it makes no sense for an energy-field to "drop off" instantaneously in that sort of situation. The energy has to GO SOMEPLACE, after all. Where is the energy stored in that field going? Electrical fields don't instantaneously dissipate... and those field have a clear and well-understood (charged-particle-exchange) method of equalizing. Where is the energy which has been stored in a "subspace field" lost to?
It's not inconceivable to imagine that "subspace energy" dissipates... perhaps even dissipates rapidly. This is certainly consistent with what we've seen on-screen (and supports the idea of the "sustainer coil" which would EXTEND the period of the field remaining effective). All you have to do is feed in energy at the same rate it's being lost (by whatever path it's being lost through) and you can retain your field strength, without having to actually GENERATE that field in the first place.
See? The entire point of a "sustainer coil" DEMANDS that the rate of "field intensity loss" is less than that required to CREATE the field. Otherwise... you'd just put "warp engines" on the saucer and the torpedos. The "sustainer coil" concept adds a relatively TINY amount of energy, just enough to keep the field from dissipating... OVER A PERIOD OF TIME.
What this means is that the field does not dissipate instantaneously. If the 1701-D saucer was able to continue at relatively high "warp" velocity to Farpoint Station, with nothing but "sustainer coils" to keep that high-power field intact... but cannot drive itself into "warp" using these same coils... then the rate of field decay must be quite reasonable.
Perhaps a "handed-off" warp-factor-six subspace field would carry the saucer along for another ten minutes without power before the field strength decreased enough to start to collapse. By continuously adding energy back into the field, just enough to counter whatever power loss you're seeing, perhaps you can continue to "coast" inside that WF6 field for a day or two before the field would eventually collapse. Maybe even (with power-consumption austerity measures in place) continue for a longer time.
So... no sustainer-coil support = faster field deterioration.
Irrelevant for a weapon being used in close-combat ("close" being defined in space-combat terms, obviously).
In "Balance of Terror" we see a weapon traveling at FTL speed... for what is really a VERY SHORT PERIOD OF TIME. In various episodes of various series, we've seen phasers used at FTL speeds... but those, also, saw only very short windows of existence.
A "handed off" subspace field in which these weapons travel is entirely consistent with this... AND is consistent with what you'd want in FTL combat as well... that is, for your weapons-fire to have a range limited by your "zone of engagement" (and to become effectively inert beyond your intended target-engagement range).
A phaser beam might be "jacketed" (and I'm not gonna call it SPADIS or whatever... I'm not "borrowing" this term from Tech Manuals, I'm using reason and a knowledge of science) in a bubble of subspace. It might continue to travel (in a linear fashion) through this bubble, at speeds well above C, for ten or twenty seconds, then the bubble would collapse. Perhaps the mere act of collapsing would dissipate the beam - if not, sufficient length of travel in real-space would result in the beam dissipating to harmlessness in a fairly short period of time anyway.
Romulan plasma weapons had a major drawback in terms of effective range... and this can be related to "spreading out" as well as to the immense power of a subspace field (relative to that used to carry a starship, which would be much smaller) required to envelop that weapon... such a field, no matter HOW powerful, would dissipate over time (with no "sustainer" device).
Had that "Balance of Terror" weapon had a "sustainer coil" device which was doing what a "sustainer coil" would do... adding in energy to compensate for lost energy... then the weapon ought not to have had such a limited range, should it have?
Implementing a "sustainer coil" approach to torpedoes would give them the ability to course-correct at FTL more effectively (if you assume that every course-correction consumes a significant amount of handed-off field strength... which is entirely reasonable to assume) as well as significantly longer range when used in FTL combat.
This also supports the TNG-tech-man supposition that "torpedoes are exclusively used in FTL combat" with only the minor caviot that in TNG-era times, it's uncommon to do "close combat" at FTL because of the predominance of longer-range "sustainer-coil" driven weaponry... he who can hit the other guy first in any engagement is the one most likely to win that engagement, after all. But since we've seen, on-screen, in TNG and in all the other series (possible exception being VOYAGER) the various ships firing energy-based weapons at FTL speeds, and in those cases always in "close-combat" situations... I think this is the best fit for (1) real science as it can be related to Treknology, (2) what's put forth in the Treknology references, and (3) whats' seen on-screen.