Edit: some typos
but more importantly - light-based interception can be re-pointed much faster then a missile can change it's own course.
> A multiple independently targetable reentry vehicle (MIRV) is an exoatmospheric ballistic missile payload containing several warheads, each capable of being aimed to hit a different target. The concept is almost invariably associated with intercontinental ballistic missiles carrying thermonuclear warheads, even if not strictly being limited to them.
https://en.wikipedia.org/wiki/Multiple_independently_targeta...
Iron Beam (this system) is designed to intercept simple rockets, artillery, and etc for cheap. The total cost per shot is estimated at 2000USD overall (including life cycle of the parts, laser, etc) compared to 100000USD for Iron Dome missile alone. It is even more for more advanced stuff like Arrow 2, Arrow 3, or David's Sling (all, including Irom Dome, of which have greater range and capability than the Iron Beam).
The issue with your system is cost.
The rockets that Iran is supplying are unguided ballistic rockets. Artillery is also unguided and ballistic. These are super cheap so its easy and economical to fire a lot of them. This is why Israel wants Iron Beam cause its much cheaper then Iron Dome.
Now lets focus on your solution. The missiles now will need advanced guidance system, maneuvering capabilities (mid course correction, path adjustment), radar and IR warning receivers, and other advanced electronics. None of which are cheap. These components also add weight to the missile, which means bigger missile and more fuel, which adds to the cost of the missile. The need to carry fuel for mid flight adjustment also means heavier missile, which means bigger missile, which means more expensive missile. So your cost per missiles goes up hell of a lot. So now you are limited to the number you can field against Israel. Now its worth it to throw up an Iron Dome against you or possibly an Arrow 2, both which are guided missiles interceptors.
EDIT: Example of the rockets that the Iron Beam is designed to intercept: https://en.wikipedia.org/wiki/Fajr-5
Counter battery is also of questionable effectiveness when most launch sites are used only once.
There's nothing new about Hamas firing rockets from schools and hospitals and Israel responding. It's difficult to exaggerate how dirty the conflict is, and in many respects always has been. It's a positive feedback look because these activities only further dehumanize one from the other's perspective, and it's compounded by people on both sides who capitalize on this dynamic for their own gain.
I have a neighbor who grew up in Israel in the 50s and 60s. If you even mention the words "Arab" or "Palestinian" she'll get visibly angry and bitter. I'm sure the feeling is mutual for many on the other side.
1) Very often the launcher is unattended at the time of launch. You wouldn't get anything but an empty weapon.
2) You can be sure that the counter-battery fire would hit a lot of human shields. Hamas *loves* human shields.
2/ like AD you can have red/green zones for pre-authorized counter-battery