Earlier quoted context omitted.
Sharing a writing system helps with communication across cultures, even when there isn't a shared language. > One can learn multiple scripts and almost all literate people know the latin script globally nowadays. If almost all literate people know the latin script, there's a benefit to writing your language in it. Of course, the switching cost is high.
Latin script creates lot of confusion in mixed environments. For example, even native speakers of English language, major language of the world, have no clue how to read aloud random texts written using Latin alphabet.
The results are likely much better than random texts using cyrillic, greek, arabic, hangul, etc.
Otoh, If they're typists, I expect they can likely type them into a search, probably sans diacritics, but that's likely good enough for searching or looking through a translation dictionary.
Greek and Cyrillic may share enough symbols that a latin script user can make due with an onscreen keyboard or a dictionary with great effort. But a completely different script would need even more effort.