It's definitely a possibility, but I think it would come at a cost. Whereas Turks and Kurds had no native script or much of a literary history so they had to adopt Latin/Arabic alphabets, the same is not true for us: we have a rich literary history spanning thousands of years. Why abandon that?
Often times as well, script is a sign of identity. Jewish diasporas all around the world used the square script even though using the native script would've been an option: Yiddish could easily be written in the German alphabet, Ladino in the Spanish, Judeo-Arabic in the Arabic.
I don't think simplicity is an argument either. The Japanese have a notoriously difficult script to learn, Kanji (Chinese characters adapted for writing Japanese), as well as two relatively simple syllabaries, Kana. It takes years and years to master Kanji but the Kanas are easy to learn. It's possible to write Japanese entirely in one or both of the Kanas, but they choose not to. Why? Because Kanji is seen as prestigious; the Japanese take immense pride in learning it (as they should). In this day and age with the advent of the Internet, it's easier than ever to learn our alphabet, which is about as hard as learning a Latin script anyway. We have no excuse.