That’s ridiculous – of course Israel should destroy villages from which rockets are fired. To call that “wrong on lebanon” is absurd.
However, of course Israel should make Syria pay for it’s support of Hezbollah as well. The two ideas are mutually supporting.
The whole world will condemn Israel for attacking places from which it is attacked? But the world WON’T go nuts if Israel starts a war with Syria who did NOT attack Israel but merely gave support to Hezbollah? Yeah, I can see the “world” accepting that! The whole premise of the OP is seriously flawed on that count.
If world condemnation is a worry, there is little to choose from the two strategies and flattening Hezbollah villages is probably better than starting a war with Syria. If effective deterrence is the main concern, then clearly BOTH tactics should be put into play and mutually support each other. Hezbolla could function without Syria, even if it would be harder for it, so attacking Syria, while a necessary step, is not enough on its own. Destroying Hezbollah’s ability to operate in Lebanon, by flattening villages it operates from, is, at this point, probably unavoidable as part of a two pronged strategy.