Why not let Israel clobber Hamas?

Question:

What if Israel decides that enough is enough and pummels the Gaza Strip back into the stone age?

Everyone seems to hate Hamas, but no one is willing to accept the consequences of a protracted military engagement to dismantle them.

Call me a hawk if you will. But, I've never believed 1) that there will ever be a time that war does not exist, nor, 2) will there ever be a time that military action is not called for. I like the idea of "quiet diplomacy" but it doesn't seem to have gotten us anywhere in the Middle East, with the notable exception of Gen. David Petraeus genius execution of the Iraqi surge strategy, which depended at least as much on Petraeus' diplomatic skills as military might. I believe it had little to do with standard American diplomatic channels and much to do with Petraeus. Hamas can't just be hunted down and shot like the Taliban because there is the debate if they are a legitimate democracy or not, although even if they are, they are still considered a terrorist organization. I see why you can't just march into someone's country and arrest or gun down their elected leaders -- talk about "illegal regime change" -- but out of the options for a viable Palestinian central authority, Hamas should be the last option, really. Do the Palenstinians even like Hamas? The Israeli-Palenstinian Conflict is as old as the Bible, but it seems to me that the PLO is the only Arab leadership body that is interested in a peaceful solution. Maybe Israel is doing the rest of the world a favor by dealing with Hamas, so nicer, more politically correct, countries don't have to get their lily white fingers dirty. So we huff & puff and act outraged and concerned, and let Israel deal with it. Sounds like a strategy to me.