Iron Dome already DOES protect the airport. Israel has said all along that the rocket that fell within 5 km of LLBG was tracked by Iron Dome and not shot down because it was not a threat to the airport. Ben Gurion remains one of he safest airports in the world. DCA, and LGA could only hope to be so safe.
I know the news that the world-wide boycott of Israel's airport has failed is deeply disturbing to Hamas supporters around the world that want to see Israel pay in some way for their step-by-step irradiation of the Islamist vermin in Gaza.
It does protect that area, but the rocket got through nonetheless ... and that’s what started the “stampede” of the airlines ... :-) ...
Since there has been no others getting through, I suspect you’ll see the various airlines (who suspended flights earlier) dribbling back to the airport.
BUT ... with travelers and tourism ... that’s another matter. In the past it has taken six months for tourism to recover.