But how expensive are those missiles? Are they meant for killing small drones?
i don't think the officers in charge of protecting the ship generally factor the material costs of doing so in to their decisions. they've got standing orders from above, and somewhere far up the chain, somebody traded off costs, lives, reputation, etc, etc. dude at the bottom has a set of rules.
Not sure about mid ranking officers, but captains who are in charge of ships think about such things.
Often times military cost per unit factors in a fixed R&D cost. It doesn't necessarily mean it literally cost 1 million in parts and labor to assemble the single missile.
Additionally, each of those Destroyers have 7 (if I recall correctly) .50 caliber machine gun mounts around the perimeter of the ship, which could also probably handle the drones.