You forget that the majority of the Lebanese populace hates Hezbollah as much as the Israelis.
It's only about 40% of the population that backs Hezbollah. You want to punish 60% of the population for the actions of the other 40%?
The polls seem to suggest the the H men have had an uptick of popularity in Lebanon, including inter alia, the Christians. This issue cannot be resolved by polls alas. Pity.