Choice of script is always about ideology. Always. It’s not about linguistic rationality. In fact, when the missionaries or linguists come to town and start devising orthographies for previously unwritten languages, one of the language communities’ frequent concerns is that their orthography should look different from the tribe down the road.
Latin swept the Middle East as a vehicle of Westernisation in Kemal Atatürk’s time. That was Kemal’s ideology: it was hardly ideologically neutral, any more than Arabic script was. Yes, Ottoman Turkish orthography was pretty damn clumsy; but that wasn’t the main reason for the switch.
And yes, there has been a merry-go-round of script reform in the former Soviet Union, from Arabic to Cyrillic to Latin. But that’s not primarily about rationality either. It’s about (a) the old link to Islamic culture being broken by Communism, and (b) the new links being drawn to Pan-Turkism. Nothing neutral there either. Moreover, given the disruption introduced through Communism, scripts there now have the Lindy effect (thanks to Adam Mathias Bittlingmayer for introducing me to the notion): the scripts are now not long enough entrenched to resist replacement.
But Persian? Why does Persian use Arabic? Because Islam. And because no Kemalism or Pan-Turkism. And because Westernisation is not as compelling to them as it was to Kemal in 1920.
I have a soft spot for Greeklish, the adhoc online Latinisation(s) of Greek (Nick Nicholas’ answer to How are Greek characters written with Latin script?). But we’re not talking YouTube comments here. We’re talking the entire literary culture of Modern Persian, all the way back to Fedrowsi. Kemal made the decision that Turkey could break with its Ottoman literary past. I’m not seeing even the most ardent Zoroastrian emigré say they’d want that.