i think i'd like to see your work there, dr slurp.
Yeah sure:
Let's assume that we are trying to defeat a massive enemy volley of ASMs, presumably from box launchers (defeating a fleet which uses full-sized ASM launchers is trivial, we've all fought the NPRs enough times to know this). A size-1 box launcher is 0.15 HS (7.5 tons), and a full-size launcher for the same size of missile is 1 HS (50 tons). Additionally, a 1-HS magazine at base tech level can contain 15 additional size-1 missiles, so the full-size launcher plus 1-HS magazine brings 16 missiles by itself for a total of 2 HS plus some amount for crew space. In that same 2 HS allocation we can mount roughly 14 box launchers, maybe 15 depending on how much space the crew quarters will cost us. So, if (and this is an important if) we can launch all 16 of our AMMs from full-size launchers before the enemy missiles hit us, the full-size launchers will break even (and slightly outperform) the box-launcher solution.
For sake of example, consider enemy missiles at roughly ion tech moving at, say, 30,000 km/s (for sake of example; building even faster missiles is not difficult at ion tech but missile doctrine is a whole other can of worms). If we have reload rate 3 through 5, we can launch a AMM volley every 10 seconds during which the enemy missiles cover 300,000 km of our sensor envelope. To launch 16 volleys we need 155 seconds (first volley at t=0, second at t=10, and so on until 16th at t=150, plus one 5-sec increment to actually intercept the enemy missiles), which comes out to a sensor envelope of 4,650,000 km. For fleet-standard RES-1 sensors this is a tall order, requiring some fairly advanced tech, but it is a fairly easy sensor envelope to create with a few AWACS fighters for instance (especially since you get to use their sensor
diameter rather than only the radius as for ship-based sensors), and you can create some extra distance by piloting your fleet in the opposite direction as well.
Once we hit Reload Rate 6 and 5-second AMM launchers, this envelope basically gets cut in half and becomes quite easy to achieve, and in fact becomes feasible even without fighters if we use a very large AM sensor. Additionally, since magazine efficiency tech improves as well it is possible to get a few more AMMs into each 2-HS launcher/magazine combo. This is not even getting into the strategic flexibility of being able to reload from a collier between battles (deep AMM magazines are a bit questionable since this limits your volley size compared to shallower magazines but more launchers).
It is trivial to also show that reloadable reduced-size launchers are simply inferior, as they cannot match the salvo size of box launchers nor the fire rate of full-size launchers. The main use of these would be using the 33% size launchers as inefficient box launchers which can be reloaded from magazines for purely strategic/logistical reasons, but frankly if you can get away with doing this it is because you are facing NPR fleets which pose no challenge for a veteran when it comes to missile defense anyways.