It would be much harder to overwhelm with multiple missiles.
You have to place Phalanx systems all around the ship in order to provide 360 degree protection. However, an enemy could concentrate multiple missiles on a space covered by only 1 Phalanx.
If radar detects multiple missiles inbound, more drones could be easily be routed to the appropriate area to intercept. To overwhelm the defense you'd have to fire more missiles than the ship has drones (and since drones could be made much more cheaply than supersonic missiles, that would be fairly hard to do).
