What's the ammo load for sustained CIWS engagement? Seems like that could be a limiting factor.
A naval CIWS generally has about 20 seconds of ammo, ~1500 rounds@4500rpm.
That said, it doesn't normally need to fire 20 seconds against a target. The system stops shooting when the target reads as no longer a threat on radar. For a mortar round, that's probably 'blown up', but even a hit that knocks it off course so that it's no longer on a trajectory that threatens to impact the protected area can cause the CIWS to stop considering it a target and move to the next.
But yeah, manage to get a dozen mortar rounds on simultaneous incoming trajectories and the CIWS system probably won't be able to stop all of them. Even if you can't, a dozen mortar rounds will probably exhaust the ammo and let the next ones through until somebody manages to reload the thing. I can't find a reload time figure for the US Phalanx system, but the Dutch Goalkeeper, which uses 30mm rounds vs Phalanx's 20mm, takes 9 minutes to reload below deck.
However, if you think about it for a moment, there's a large, large difference between lobbing a mortar or two at a base and launching a dozen synchronized. You then have the "problem" that the less synchronized your launches are, the more that the system can handle, and since it'll be nailing the ones that would hit first, that enables the people on the base(the true targets), to get under better cover before any manage to hit to do damage.
For that matter, while you might be able to move a couple tubes without being seen, moving a dozen is more likely to be spotted, and again, that enables the personnel to get under cover. So the system, even limited, drastically increases the costs of successfully attacking the base.
