Yes, that is what we wish we could and would do. Life is so much simpler in black and white. Unfortunately, we are frequently forced into gray areas.
What if they took us up on our dare and chose China? Would China take their side in the current and probably continuing conflict or would they quickly facilitate the extinction of Israel? Since the Arabs are fighting us I suspect China would back them. With Israel gone and the Arabs emboldened and backed by China what would happen to Iraq and the rest of the area? In my view it would be forced to join China and the terrorists and make our security much in doubt.
Life ain't easy and hasn't been since Eve decided to push apples.
Israel can do the calculations as easily as you, and given the choice can calculate that choosing China over the U.S. would likely be suicidal for them in the long run; and thus it is not likely a choice Israel would make.
Second, the chances that jettising automatic support for Israel (over its sale of arms to China) would hurt us in Iraq is laughable in as much as the Iraqi's who are fighting the insurgents are fighting for a democratic based government and the prospect of a democratic based future.