re: PLAN Type 052 Class Destroyer
Well, look at the LD2000. There is a model with 3 short range missiles strapped to each side of it. If it was really deemed necessary to have both gun and missiles, they could do the same thing for the naval 730s almost overnight.
As for supersonic AShMs doing terminal maneuvers, well I seriously doubt something massive like the Brahmos would be very good at it even if it could do it. But extreme end-game maneuvering is certainly one of the big selling points of the Klub. But the point I was making was that the faster a missile is going, the longer a gun-based system would need to lead it, and that means even small changes in speed and/or vector could easily be enough to spoil a shot. Certainly, a faster missile would not need to maneuver anywhere as much as a slower missile to spoil a shot. Also, subsonics rely more on saturation than end-game maneuvering to defeat modern, layered defenses.
Also, gun based CIWS can engage multiple targets at the same time. You could easily set the gun to automatically fire off 1-2 second bursts at multiple targets, and then switch back to fire more bursts at anything the first bursts missed.
You will have a more limited firing ark as the turret itself needs time to traverse, but in that narrow field, you have the advantage that your shots are going against exactly the targets you want, whereas will missiles, there is always the chance some missiles might all go for the same target.
I am also unconvinced about just how well missiles like SEARAM would cope in a saturation attack scenario where AShMs are exploding left right and center as they are intercepted, but more are still coming in seconds behind the destroyed ones. Can their IR sensors even still function when a ton of HE just went off in their face?