Box launchers (to me) serve three main roles.
1: Salvo Saturation - Link your boxes to the same firecon as your normal launchers, and get a lot more firepower, but only once. This can be useful to overwhelm a heavy defense, such as if the enemy has heavy shields or good point-defense, then a massive salvo can overcome it. Or if you simply want the joy of overkill~
2: Fighters - Being tiny, you might get a size 1 engine, another ~2 hull for life support and fuel and firecon, and have 7 HS remaining for missiles. You could fit a size 1 launcher and 6 HS of magazine, which might give you, let's say, 7 missiles total. Comparatively, if you mounted box launchers, you could fit like 50 size 1 box launchers into 7 HS (Unless my math is off, which does happen). At .15 HS each, that's a lot of tiny missiles, and makes for some fair point-defense platforms as long as you have enough fighters to support the incoming fire. Or sandblast the enemy's armor. Or mount like a size 50 single launcher and use a fighter to deliver a massive payload. Just return to hangar to reload.
3: Specialty Ordinance - Namely minefields, planetkillers, and sensor drones. You can very easily mount a few box launchers to have a minelayer toss a dozen buoys somewhere. Or mount a box launcher for a 0 fuel missile (1 second lifespan makes it an orbital bomb) so you can load a huge warhead to drop on a planet and wipe out the population. Since you probably don't need more than one of these, they're nice to box mount. Or, my favorite, design a drone and make the second stage into a buoy with a sensor. Fire the drone at a waypoint, and when it arrives it deploys into a sensor buoy, very useful for putting a thermal sensor where you think the enemy is, so you can tell if there's enemies there or not and some idea of the size. Or an active sensor, but chances are you'll get that buoy shot down. These "special ordinance" are usually, well, special, and don't need to be used very often, so reload is often not worth the time.
Sometimes a .25 size launcher will suffice, but sometimes boxes just fit better.
Also note that you should have no reload on your box launcher. Since reload tech doesn't effect boxes, you can increase the research and resource cost of your missile tube without gaining anything. Default is "best tech" so you need to set it to 1 reload to avoid overspending.