Timo made a good point in another thread. I didn't want to derail that Romuland thread, so I'll answer here:
Regarding the tech aspects of the silly extra torp launchers, one might say that they were a lesson learned from the Dominion War. Apparently, starship phasers didn't do as much good against the smallest Jem'Hadar ships as they should - and phasers used to be the primary defensive weapon. Perhaps the solution was to take torps from offensive to defensive, and to add small, short-ranged torpedo weapon systems all around the various ships for self-defense purposes?
Note that we have seen the tiny runabouts fire torpedoes, too - although never at warp. Perhaps sublight torpedoes don't need big launchers with long accelerator barrels? The newer torps of the E-E never did warp. Nor, for that matter, did the quantum torps of the E-E ever get fired at FTL speeds.
Timo Saloniemi
That's a very good observation and hypothesis. Even the quantum launcher, if you look at the MSD, seems to be small, and the torpedoes are dropped into the turret from above. It could be that, while quantum torps are more powerful and/or have a penetrative quality, they are slow, low maneuverability, short range weapons that can't travel at warp, hence the need for backup in the form of 4 other tubes. When you look at Galaxy-class, those launchers are 40-50 yards long, something's gotta give.
This would all fit with the facts we see on screen:
In First Contact, they fire 4 quantums at the sphere, why not just use the photon torpedo tubes? May be they have good penetrative ability in addition to being more powerful since we see them sort of explode from the inside of the sphere? This also begs the question, why use quantums on the Phoenix? Wouldn't one photon be enough?
They seem to be fired from short range. Defiant fights in close quarters by definition, so they appear little faster when fired from Defiant, since the distance between the two ships is short; in First Contact, however, they look pretty slow on all three occasions they are fired, especially where the distance is a bit long: against the sphere and the Phoenix.
For what it's worth, even though books are not cannon, it's interesting to see other authors' take on it. In the TNG "Dominion War" books, the author thinks it's necessary to drop the shields, before firing quantums, which are also fired from the aft. At that time I used to think that the aft launcher must be the docking port above secondary shuttlebay.
In "Ship of the Line", Picard asks for phasers and photons. When informed that photons are off-line for the next few hours and they "only" have quantums, he says that quantums are not manueverable enough, and asks for everyone to concentrate on fixing phasers.
It's obvious that the earlier opinion was that they are somewhat different, special if you will, and not a direct replacement for photons.