The firing arc thing works better when there's also shield and/or armor arcs (as in SPAZ, iirc, though I may be misremembering).
Also when there are multiple active weapons.
And when turning isn't something that's done as easily as it is in TLF.
And in general when all ships don't act essentially as fighters (all firing from the central point, all very maneuverable in terms of turn radius and acceleration, none of the combatants massively slower than average, etc).
I'd certainly like all of the above, as capital-ship combat is far more interesting to me than fighter combat, but just adding in firing arcs by themselves probably would seem a bit like it sat down between two stools.