That would be a huge mistake for Israel. We are the only thing stopping them from becoming a pariah state and they return the favor by slandering our leaders. Israel needs new leadership, from the left-wing.
There isn't going to be a left-wing Israeli leader again, at least not in this generation. Ehud Barak and later Ehud Olmert poisoned that well completely. You can't win an election when you lose the security question by 60%. If Netanyahu - arguably the weakest potential Likud leader - won reelection decisively with low poll numbers and the American President actively encouraging his ouster, the right isn't losing any time soon.
That being said, they'll definitely be better off once a moderate right-winger like Nir Barkat takes charge.
When did Ehud Olmert become left-wing? Obama and this administration, like stated above, has defended Israel like all others before it. Without Obama and the UN Ambassador, Israel would be screwed. Russia will not risk their allies in the Mid East in order to become the new guardian of Israel, so America is all Israel has, and intimidating one of the two parties isn't helping. If Israel wants to become more right-wing with a nut like Bennett, fine, but expect further decreased support from the Democratic Party. Israel can't afford for it to become a partisan issue.
Diskin, Ashkenazi, Gantz are all possible alternatives to the current left-wing establishment. It's amazing Herzog did as well as he did, so all hope isn't lost. And yes, a moderate right-winger could be good too, but do you seriously see Likud becoming more moderate?