[H]itting the Iranians in lawless Syria is one thing, in line with the general contours of Israeli activity and defense strategy in recent years. An Israeli attack in Iraq is another, constituting a significant expansion of the military theater.
The Israeli security establishment has been acutely worried in recent months by growing evidence that Iran is using the Shiite militia infrastructure in Iraq as a pipeline for weapons transfers to Hezbollah, which menaces Israel from the north in Lebanon, and as a holding point for ballistic missiles that can hit Israel all the way from Western Iraq.
Armed to the teeth, the various militias could be used as a tool to pressure Israel, but also be presented to the world as independent actors, lending Iran plausible deniability. Israel is familiar with this strategy—employed by Iran with Hezbollah in Lebanon—and it’s determined to prevent a repeat in Iraq.