>>The Block 1A and newer (pneumatic driven) CIWS mounts fire at a rate of 4,500 rounds per minute with a 1,550-round magazine.
>>Shells fired by the Phalanx cost around $30 each and the gun typically fires 100 or more when engaging a target.[14]
>So it's about three grand to zap one drone, and you get 15 shootdowns before a human needs to shovel more ammo into the turret. That would make it vulnerable to a saturation attack.
You could imagine firing fewer rounds per salvo, but that only slightly mitigates it. Against drone swarms you kinda want directed energy weapons, either microwave or laser. Which don't exist, currently.
Also note that Phalanx is radar based, leaving it open to the usual suite of radar jamming/ECW/antiradiation attacks.
You can tip the odds back in your favor by emplacing more Phalanx systems, but at ten million bucks each, that limits you to stuff like defending small-size/high-value targets like the White House, rather than numerous and sprawling US military bases.