Depending on how you count them, there are two, three, or more varieties of Muslim. The problem with the nuke them all and let God sort strategy them out is, it lacks the fine, but critical gradations with which they see themselves. Not covered by the media there are significant Muslims who are as much endangered by what we call radical Islam as we are. I’d like to point out that the west has no competing theology and is fractured and incapable of mounting the sustained effort that must follow to ensure success. There are 1.5 billion Muslims, quite a few of which are voters in the Western world. Imagining a conflict where the opponent does what you need him to is a losing strategy.
All muslims, everywhere, of all sects, all depend on the superiority of their Allah over all other gods. Allah determines everything down to the atomic level. To utterly destroy their most holy places, utterly defeats the central tenants of Islam - in effect humiliating their central beliefs, leaving them without Allah who allowed himself, as embodied by the Kabbalah, to be destroyed by what they all believed to be lesser gods (Allahu Akbar - my God is greater then your god).
Shortly after 911 and group of jihadis in Afghanistan were asked the question above, and replied they would all convert to Judaism, Christianity or become atheists.