Though the cease-fire in South Lebanon is fragile, it's paramount that the agreement holds so that conflict between Israel and Hezbollah isn't reignited. Israel will withdraw from Lebanon, though both sides have likely violated the cease-fire in some cases. Nonetheless, this war must come to a permanent end.
Hezbollah hasn't been defeated and is quickly reemerging along Israel's border. Indeed, the "cease-fire" only served to give Hezbollah cover and time to organize when it was in disarray following Israel's destruction of its leadership. Hezbollah is exploiting the situation to make political gains in Beirut and reassert its presence in the south, thus why Israel must maintain these points along the border.
Israel is violating the cease-fire, and the Lebanese government is allowing them to do so. Indeed, this new government, handpicked by the US and Saudi Arabia, is more concerned with tying the hands of the Lebanese resistance to protect Israel than it is with maintaining Lebanon's sovereignty.