Actually, we should let Israel do the honors, and then we join up after the New Year, giving our guys some R&R while the IDF explores their newfound territory. This stuff has gone on long enough...
I'd love to see Israel take Syria to task for it's support of the Hezballa and other terrorist groups, that have attacked it for decades. Israel is such a super-charged topic for the middle-east, I think it would set back our efforts decades if we were seen to support this.
IF the world saw the middle-east clearly, understood the dynamics as we do, I'd be more inclined to agree with you. Europe thinks Israel is the bad guy. Russia has been a long time ally of Syria. Each of these factions would support the theory in the middle-east, that the U.S. had been fronting for Israel all along.
Right now we have fairly friendly contacts with a number of the governments in the region. If we were to advocate Israel taking military action, that would probably end immediately. We'd wind up against the world, with Israel taking massive amounts of blame.
Would this be justified? Heck no. Israel would be giving pay-back for decades of dead bodies piling up inside their borders. (in effect) Sadly, unconcionably, incredibly, the memory of Syrian support for Israel's attackers would evaporate the moment the first shot was fired.
I don't know what the cure for this is. I guess we're stuck doing the heavy lifting, which is actually very favorable for Israel. Right now we have a justified reason to be doing it, after being attacked. And if we can bring peace and prosperity to Iraq, perhaps things will look up over-all for the middle-east.
Do I agree with your sentiment? Yes. I just think we'd both be mistaken to back what we desire to se.