The unified writing system is a way to keep the nation unified and able to read the same texts. Yes, it does require that a very large sub-group learn a totally different written language. But Switzerland has made a similar calculation. People might speak Swiss German at home and on the street, but all formal writing is done in Hochdeutsch, "standard" German. It's hard to find a book written in Swiss German, and kids essentially have to learn two languages. But as a result of the extra learning, a Swiss German speaker can communicate with German speakers from all over, rather than being able to communicate only with other Swiss.