We've also seen phasers used at FTL speeds, even in TNG where it was established that phasers were sublight-only. This isn't really outrageous, any more than anything else we've seen. My personal "preferred explanation" is that the phaser cannon actually have the ability to 'jacket" a beam in a subspace field, allowing them to exceed C (by a level directly related to the strength of the passed-off field).
Another option is that in FTL situations (or non-FTL situations for that matter), the computer lock for the phasers "leads" the firing of the phasers such that the computer fires the phasers at the location at which the target will be when the phaser beams reach that location.
Kind of like firing a rifle at a moving target. You have a fire in front of the target in order to hit it or the bullet will fly behind the target.
YMMV
The problem with this approach is that the phaser shot, if it really IS purely sublight in nature, would be trivial to avoid if your ship is moving FTL and this were the case. The best "in-universe" example of this would be in "Wink of an Eye" where the accelerated people prove able to merely step out of the way of a hand-phaser shot.
For phasers to be effective in combat between ships moving at FTL speeds, you'd either need to fill a volume of space with shots (so it would be like trying to walk through a rain shower and avoiding the droplets) or you'd need to be able to have your beams move faster than the ship you're shooting at.
Despite the supposition that it's "stupid," this second idea isn't as far-fetched as it apparently seems to some. An analogy to look at this through would be to think of your "subspace field" as a bubble... I say that often enough. Now, imagine how a bubble can be dragged through the water, attached to, say, a reed.
For a Romulan plasma torpedo, for instance, you'd only need to generate this subspace bubble and shoot it out, with the plasma weapon inside of that bubble. Yes, the field will lose strength over time, and eventually the weapon will fail as a result. But there is no reason to pretend that "subspace fields dissipate immediately unless consistently provided with power." Trek-nology has dozens of cases we can look at where this is established NOT to be the case, doesn't it?
There is absolutely no reason to assume that subspace fields collapse instantaneously upon removal of driving power. None. Zip. Nada.
So, why not "toss out a bubble" with the weapon inside? The only reason you'd need any physical influence on that "bubble" would be if the weapon needed to be steered.
For a phaser shot... not an issue. They just fly straight and true, as will any "beam" weapon.
For a torpedo, the only thing we know for sure is that in the TNG-era, these torpedos have "sustainer coils" but not warp drive coils... meaning that they have to receive a "handed off" subspace field (aka "bubble"). In TOS, they may not have had the ability to steer (definitely the case if they were energy-weapons only) but could easily still move at FTL. I'd assume that the TWOK-era "physical torpedo casing" was an improvement... more expensive and more space-consuming, obviously, but far more likely to actually strike the target, since it would have LIMITED capability for course-correction, and (since it would be adding small amounts of energy to the handed-off subspace field) probably significantly improved range at FTL (though of course, still "infinite" range, once dropped back to sublight velocity).
Now, for a Romulan plasma weapon.. that's somewhat dubious. That is, we see no clear evidence on-screen that the crew tries to avoid the weapon... just that they back away from it and try to outrun it.
So, the question that really comes to mind for me is "why didn't the Enterprise simply turn 90 degrees and try to sidestep it?" It's quite clear from the dialog in the episode that nothing of that sort was TRIED. They simply tried to "outrun" it.
The only way that makes sense is if the plasma weapon was wide enough that it would have been impossible to avoid. Definite hard to imagine when you're talking FTL velocities, true.
If you go back and "retcon" the episode to insert some "evasive maneuvers," it would become clear that the weapon had steering/tracking capabilities. But there's nothing in the episode itself which states, or even really infers, that.
If the weapon spreads out to blanket a wide area, and moves extremely fast... an analogy would be to think of the weapon as a broom, and the Enterprise as an insect. The weapon "sweeps" through space, and the Enterprise tries to run away, but is so slow (relative to the "broom") that no matter what direction they run, they'll be swept over. They just got lucky insofar as the length over which the weapon "sweeps" is fairly short... possibly so that the beam's "cone" is something like 30 degrees... resulting in the width of the beam being twice the length it's traveled.
Given a situation like that... where you'd know you couldn't outrun it in ANY direction... "backing away" would be the only possible solution, since you could easily conclude that the beam strength (per unit projected area) would be decreasing significantly with range from origin. This would be even more of an issue with a plasma weapon, which would be "cooling" all the time, and would also be dramatically impacted by the presence of a subspace field which was decaying over time as well.
with computers inside and whatnot was involved.
