Reduced to its essentials, the IDF strategy may be ridiculously simple: fix the Hezbollah force in Southern Lebanon while detaching its command structure from the field by simultaneously striking Beirut. One of the great mysteries, upon which newpaper accounts shed no light, is why the IDF should so furiously pulverize Hezbollah's enclaves in southern Beirut, blockade the port and disable the airport. The object isn't to shut down Lebanon. It is to momentarily disorient the Hezbollah headquarters in Beirut, so that in a moment of absentmindedness, the Hezbollah forces in Southern Lebanon will do what comes most naturally: commit themselves against the IDF.
I also believe that in order for Israel to destroy Hezbollah now and future, they will need to do more than just "disarm" Hezbollah. Part of Hezbollah power, both practically and public relation wise, are the social services Hezbollah provides in Southern Lebanon. Practically, they are the de facto government in Southern Lebanon because the central government of Lebanon cannot "keep the trains running on time" sort to speak. And this translates to political power that grants them legitimacy regionally. And this also has endeared them to Europe, granting them international legitimacy in the eyes of some as well.
Thus this war presents a second opportunity for the central Lebanese government to reassert itself in Southern Lebanon. With international assistance, primarily US but also EU, the central government should do all it can (without Hezbollah) to rebuild and provide for Southern Lebanon after the ceasefire and while Hezbollah seek to rebuild itself and its paramilitary infrastructure.
This is how Hezbollah can be destroyed. Degrade its military forces in war; marginalize its social services in peace. Have to win both.