I’m not sure why the Israeli’s didn’t employ radar directed AAA as an initial line of defense against these rockets?
Because it would wake up sleeping children.
That’s a credible idea. Similar to CIWS but using the larger HE shells AAA offers. If I had to guess I’d say there are limitations of accurately setting the warhead’s fuse along with the high CEP of inertial targeting for a ballistic target interception.
Slight variances in AAA muzzle velocity may also pose issues for successful interception.
A missile otoh can make the necessary in-flight adjustments to its launch solution for greater likelyhood of interception.
Similarly, spamming HE CEWS would likely incur higher collateral damage.
Same problem as everyone else has had with AAA - what goes up must come down and given the trajectories, you’re going to be getting a lot of ordnance landing on Israeli territory that missed or failed to explode.