The first thing one does in war, especially a war with Arabs, is to cut the command and control lines, so that the people in the field can't get good orders from their leaders. Thus, the airports and communications facilities.
The second thing one does is to cut supply lines so that the people in the field can't be resupplied. Thus, the bridges and roads to Syria.
From Wikipedia. Areas you have specified as not containing Hezbollah are actually pwned and operated by them.