Fezzes would probably be a lot more common, if it wasn't for the influence of Ataturk and other secular nationalists. Initially, the Ottomans and other Muslims adopted fezzes to wrap their turbans around. During the reign of Sultan Abdülmecid I, however, in the 1830s -- when the Janissaries were abolished, and the Ottoman New Model Army was formed -- Western-style standardised military uniforms were adopted, along with Western formal and business attire (for men, at least). The one thing which set Ottoman official + military dress apart was the fez, which was retained (sans turban) to fulfill the Islamic expectation that men keep their heads covered.
This actually spurred some minor controversy at the time, since without the turban, the fez might fall off during prayer. But regardless, the fez became widely adopted by Muslims around the world during the 19th and early 20th centuries, and the fez itself became associated with Islam and (in the minds of Westerners, at least), general "Oriental" vibes -- to the extent that colonial troops from cultures which weren't even Muslim were given uniforms which included fezzes (e.g., British and German East African troops). Incidentally, this was also around the time that the crescent became widely seen (by Muslims and non-Muslims alike) as a symbol of Islam, even in places far removed from the Ottoman Empire.
The fez was banned by Kemal Atatürk, as were so many other aspects of Ottoman and Islamic identity. It fell out of favour in the Arab world for multiple reasons. In Egypt, it was associated with the much-hated monarchy; in Iraq and the Levant, with the Ottomans and with the British/French Mandates; and in the Peninsula, it was never all that popular anyway; (though it's still going strong, sort of, in the Maghreb, where it was invented). Secular Arab nationalists like Jamal Abdel-Nasser or the Baathists had little love for it. So the fez today is seen as just kind of quaint, for the most part, where it was once as expected in formal settings as a necktie.