A proposal to counter the terrorist nuclear threat

I'm not saying this is the way to go, and I'm sure that it wouldn't happen anyway, but here's something I thought of to counter the potential for a terrorist nuclear device being detonated in a US city.

The US makes it known that if a nuclear device is detonated in a US city, we will wait one day and then destroy Medina with a nuclear strike. If another nuclear device goes off after that, we will wait one day and then destroy Mecca.

Would this work? I don't know but it's interesting to think about. Mecca and Medina are the two most holy cities of Islam. Will Islamic terrorists risk the destruction of these two cities? They wouldn't care about the inhabitants; those killed would all become instant martyrs after all. But the cities themselves and the holy sites they contain would be destroyed, and would be rendered dangerously radioactive for some time. The loss would be irreplaceable.

Of course, like I said, I can't imagine this policy actually being enacted. After all, it would enrage all Muslims everywhere, not just those that condone and/or support terrorists. It would doubtless be denounced by most, if not all, other nations in the world and the UN. There are other reasons, not least of which is that it just isn't in the character of the US to do something like this. It makes for an interesting thought experiment, though.