Excellent point!!
I know. They haven't been "Persian" since sometime around 632 A.D.
Quite so. It was Islam that finally dealt the death blow to Persian culture. It's true that the Persians created a magnificent civilization, a thousand years before the infection by Islam. But then again, most of the world was better off before Islam, and not just Persia.
Persia was doomed. Had the Greeks and others not done it, the Muslims would have anyway. For Muslims to decry the loss of Persian culture is just plain funny.