If someone nuked Washington DC, would that end the United States?
Uh, no. And therein lies an important difference. The United States has much substantial basis in objective thought and practice. Those pillars stand, very much independent of any icons. Islam, on the other hand, is a hyper-superstitious cult which thrives on its icons and implodes without them. So I don't like the analogy at all (notice I did not insult you by calling it absurd or fatuous or ignorant or misinformed or moronic -- nor should I, since I do not know you nor all the vagaries and permutations of what it was that you meant; plus, for all I know, you may be the world's leading expert on Islam and know things about it that I don't, having only made a mere 30-year study of it).
If someone nuked The Vatican, would that end Catholicism?
Uh, no. And therein lies the most significant difference. Again, I don't see the analogy. Catholicism, despite its minor dalliances with various icons, ultimately stands or falls on the Gospel, which is the Good News that the bad news of man's fallen condition has been remedied, for those who believe, by God's forgiving and loving heart and the power of the sacrifice of Jesus Christ, His Son. Nuking the vatican would not change that. The Apostles' Creed would still read in the same way, and so would the Bible.
Not so, though, with Islam. A religion with Five Pillars-reduced-to-three would collapse. So would a religion whose adherents universally hold that Allah exerts supernatural protection over the Grand Mosque and the Ka'aba, in the event that it were all vaporized.
What you would do by bombing these sites, is to unite the Muslim world against the Christian world, something that against all propaganda to the contrary, has not happened.
What we have here is a fairly large straw man which I did not build. It is a rather large jump to go from a pissed-off Israel nuking Medina and Mecca in response to some dastardly deed committed by Islam or its elements against Israel, which is what I wrote, to uniting the Muslim against the Christian world, as you adduced without warrant.
By the way, contrary to your assertion, the Muslim world is united against the Christian world. The anti-Christian verses in the Koran are sufficient for that, and, if they were not, their wild-eyed equating of Christianity with the Medieval Crusades would seal the deal.