In 2006, we bought Israel a month of time to deal with Hezbollah in Lebanon. Even Arab states were quiet about the Israeli counter-attacks. But Israel failed to use their army to destroy the Hezbollah rocket-launching points, their air force failed to suppress the rockets, and in the end their punitive strikes against Lebanese infrastructure failed to push Lebanon's government--which was incapable of doing so in any case--to rein in Hezbollah. All that infrastructure damage did was compel the Arab world to end their tacit approval of Israeli actions and vocally oppose Israel.
Now Israel hopes to repeat that failed punitive strategy if it comes to war with Hezbollah again:
Israel has quietly reminded Lebanon recently that if Hezbollah attacks Israel, the retaliation will include all Lebanese infrastructure (roads, bridges, power plants and military assets). This strategy recognizes that while Hezbollah only rules in the south, the radical Shia militia makes use of all infrastructure in Lebanon. While this is true, the Lebanese government is also in a difficult position when it comes to controlling Hezbollah. That's because Hezbollah represents the minority Shia and has long used religious fanaticism and financial and military support from Iran to dominate the majority (a fractious collection of Christian, Sunni and Druze groups). The majority wants to cut Hezbollah down to size, but they don't want to wreck the country in order to do it.
What's the point of this threat? How many Lebanese Sunnis, Druze, and Christians are happy with Iran's proxy running their own state-within-a-state in southern Lebanon and paralyzing the nominal national government in the process? The government is too weak to take on the unified and ruthless Shia Hezbollah backed by Iran. Destroying Lebanon's infrastructure will not make Lebanon's government magically strong enough to fight Hezbollah.
Israel would do far better to reassure the Lebanese government that if Israel has to go into Lebanon, Israeli forces will narrowly target Hezbollah and try to avoid collateral damage. Do that and Israel will find that it has Arab governments largely silent on the fight and many weeks to complete the destruction of Hezbollah.