There are a lot of factors that affect whether or not a community changes its language. Prestige associated with the native language as opposed to another language plays a big part in it. Before the Islamic conquests, Persians ran the most powerful empire between Rome and China, and Persian culture and administration were hugely influential in the new Islamic empire. You also had native Persian dynasties founding their own states within 200 hundred years of the Islamic conquests, and they all supported the Persian language.

Compare with Egypt, that hadn't been ruled by a fully native dynasty for a thousand years by that point, and had been a province of the Roman Empire for over 600. Even though Egyptian was still a written language, and still spoken by most of the population, for all of that time it had to compete for prestige with Greek, which was the native language of the Ptolemaic dynasty, the lingua franca of the entire eastern half of the Roman Empire, and considered prestigious even by the Latin speakers who conquered the Greek world. And there was no Egyptian-speaking dynasty that rose up in the wake of the Islamic conquests.

I can't speak for other factors, but Persian definitely had an advantage in prestige over Egyptian.

Regarding Urdu, it's actually a case of a language spreading due (ultimately) to Islamic expansion. It has it's origin in the languages/dialects of the Gangetic plain, not the Indus, and developed as a heavily Persianized (which includes a lot of Arabic words via Persian) common and eventually court language under Islamic dynasties of Turkic origin, who were heavily influenced by Persian culture, to the point of using Persian as the main language of government and culture. Hindi split off later as a de-Persianized version, and Urdu became more and more specifically associated with Islamic India. That's why it's the national language of Pakistan - Urdu isn't native to any part of the country.