I got a serious problem with "Naturally, Israel would rather the Syrian government fall.". It betrays deep misunderstanding of what Israel actually wants and what would benefit it (which makes all the rest suspect too). Weak Assad would benefit Israel greatly. Despite all the saber-rattling, Syria would never seriously think of going to war with Israel, because that would mean the end of the current Syrian regime. Helping Hezbollah? Sure. Passing weapons from Iran to whomever that could hurt Israel? No problem. But direct conflict? No way. Cold war is the worst Assad would ever do.

However, everything changes if Assad regime falls and rebels - among which would be such organizations as Syrian Islamic Front or Syrian Islamic Liberation Front, with predictable amount of love for Israel - were to come to power. They would have no experience of losing the war like Assad regime had, and no problem with suffering a bit more of mayhem is it's for the good purpose - after all, that's just what they did right before it and succeeded. And they'd own all munitions that Assad regime had assembled (at least those that left after the war, but there would probably be sizeable amount left, and if not, Putin could help), including WMDs. How there's any benefit for Israel in that?

Israel would be glad to have Assad's ass get some thorough kicking. However, having an explosive unstable government with WMDs on its borders is not exactly one's dream. Israel already has this problem with Lebanon, and it didn't work that well so far. Having second one is really not anybody's wish.