Probably because Persian is an Indo-European language, and alphabets are better than abjads (alphabet without vowels) for it.

Semitic languages are easy to write without vowels because the meaning is very obvious even if you omit the vowels, but in many languages you have a great deal of collisions if you omit vowels.

It's the same reason Chinese characters are a poor fit for Korean and Japanese. Chinese is not an inflected language so one symbol for a word works quite nicely, but other languages need a way to add prefixes and suffixes to works.