While a sultan(a) is a Muslim sovereign, there is no secular head of government in a sultanate, so there’s not really an alternative non-religious title. Separation of church and state became a widespread practice relatively recently, so most of the exotic, cool-sounding titles that the writers have to choose from most likely had religious connotations. The most well known use of the Exarch title is by the Eastern Orthodox Church. For that matter, the monarch of the U.K. is technically the head of the Church of England. It’s just a word that sounds interesting but not made-up, and has the middle eastern aesthetic that they wanted to use for Ul’dah. Also Ishgard uses all the catholic titles. SE has always repurposed cool sounding words into whatever they want them to be, building on their own meta use of these words throughout their games.