The tech manuals can be helpful in filling in blanks, but they have been contradicted on numerous occasions by the episodes themselves. And if we're going to include the tech manuals for TNG, then what about the writer's bible for TOS? Phasers were originally described as an offshoot of the asteroid deflector beam technology which a starship much apply when at warp. As the deflectors must by neccessity be FTL, so must the phasers.
The deflector beam wouldn't be FTL with respect to the ship that fires it. Relativistically speaking, the lightspeed barrier still applies for a starship traveling at warp speed (not to an outside observer, of course, but relativity is weird that way).
Secondly, starfleet officers rarely target their foes manually
They do in TOS, hence Sulu's targeting scope on the helm.
OTOH, no one's talking about manual targeting. The sensors that automatically aim the phasers can only track targets with the data available to them, and the probability of a hit depends on a combination of how precisely you can pinpoint the enemy's position and how precisely you can control your aim. At 200,000km, a 200 meter target would have a cross section of a thousandth of a nano-arcsecond; your phasers' aiming mechanisms would have to be calibrated to within a fraction of a nanometer to get that kind of precision, and that for hitting a target that's STATIONARY. If your ship is MOVING, all bets are off: you need to know the exact relative velocity between your ship and the target, and an uncertainty of just a few meters per second can throw off your aim by tens of kilometers, even if your fire control system has that kind of precision. And it probably won't; on the same scale, a submicron spec of dust on one of the bearings can throw off your aim by the same degree, and rotational component in your own vector too small for even your navigational sensors to detect can mean your phasers fly wide of the target by a hundred kilometers.
I cannot overstate the kind of precision you would need for that kind of shot; it would be like performing brain surgery on a mouse... from sixty feet away, looking through a telescope.
More relevantly: any good targeting system isn't going to be built for precision, but for SPEED. Its job isn't to work out the position of a distant target to an insane degree of accuracy, but to quickly LOCATE the target and plot a best-fit firing solution for as many weapons as you can point at it.
the computers and sensors do the job - and they should have no trouble tracking a FTL opponent
Tracking and HITTING are two different things.
A final word on the seemingly massive ranges employed by TOS - at the time of the series production, typical aircraft carriers and gunboats ranged their weapons over many miles, some even to the limit of the horizon. Would it not be natural to extrapolate these distances into their outer-space equivalent?
No, for the simple reason that space doesn't HAVE horizons and the limitations on weapons technology is going to be considerably different. It would also depend on what kind of weapon you're using; phasers and photon torpedoes are direct fire weapons that seem to require pretty accurate firing solutions and therefore aren't much better than guns and rockets.
OTOH, there ought to exist a Trekian cruise missile of some type -- say, a weaponized version of the Class-8 probe -- that can travel interstellar distances at warp speed, search for a target and autonomously guide itself towards an interception point. Such an weapon could have an effective range of hundreds of lightyears and could even be programmed to wander around the outskirts of a solar system for weeks at a time until it found something that matched the profile on its list of approved targets. That's the kind of weapon you would fire at a distance, not from 200,000km, but from two or three AUs where the thing will have a flight time of twenty to forty seconds and its hapless target will be forced to deploy countermeasures and decoys, or risk shooting it down (either by launching smaller/anti-missiles to intercept it or by trying to kill it with phasers at the last second), or go to high warp and hope against hope that they can outrun it.
That, of course, would be a fundamentally different take on combat in Star Trek; it would be like a combination of submarine/surface/air-to-air warfare all the same time, with starships that spend entire battles running from one another's torpedoes while at the same time trying to find an opportunity to get in close enough to punch each other's lights out with phasers. There'd undoubtedly be different sizes and classes of torpedoes too; smaller torpedoes for hitting small/nearby targets or for knocking out other people's torpedoes, and larger anti-ship torpedoes that can you launch against a target on the far side of the solar system. Other equipment would be of high necessity; the cloaking device would be indispensable, not merely for sneaking up on other ships, but for avoiding the roving spreads of torpedoes they keep firing at you (whose AIs surely have a general idea where you are but can't home in for a kill). Decoys would be needed too, equipped with a convincing hologram or even some kind of replicator that can create a facade of a proper target and lure a torpedo away from the real thing. Starship combat tactics would be as much about securing your exit path as it is about watching for potential enemies, much less of the simple "bad guys there, they're firing... shields at 80%... return fire" formulaic business we're used to.
I do agree that star trek combat is less and less realistic as time goes on, but my gripe isn't that the ranges are getting shorter, it's that it's always been way too simple, and throughout TNG and DS9 it's been getting simpler all the time.
