tl;dr
The Quran is by definition in the original language. A rendition of the Quran in modern Arabic would not be the Quran at all.
Deets
It is generally accepted that the caliph Uthman ibn Affan established the canonical version of the Quran by 650 CE, within two decades after the death of Muhammad. This established the text's 114 surahs (chapters) and their ordering. Since then, the Quran has been considered complete and closed, disallowing any possibility of additions, deletions, or alterations to the canonical text.
The Quran in its original language is considered perfect and inimitable. Any attempt to render the Quran in any other language, no matter how faithfully, is at best an interpretation, at worst a heresy. From quran.com:
The Quran has been translated into over 100 different languages, and each translation can be considered its own interpretation of the original Arabic text. It is important to note, however, that the Quran is the word of God and is therefore sacred and unchangeable. As such, translations of the Quran are intended to convey the meaning of the original Arabic text as accurately as possible, but they may differ in their interpretation of certain passages.
emphasis added
The form of Arabic used in the Quran, classical Arabic, is not a vernacular language, and perhaps never was. Rather, it is a sophisticated literary register, analogous to medieval Latin or classical Sanskrit. Over the course of the centuries, locally spoken versions of Arabic have deviated widely from classical Arabic. As @Medi1Saif remarks in a comment:
today nobody or in no country people speak fasih or what is called standard Arabic, this language has been more and more put aside in favour of local slangs, so the Arabic of the qur'an my be found at schools and in newspapers and on tv in the news, even in chats and online it is vanishing.
Despite the growing gap between spoken varieties of Arabic and the language of the Quran, the belief in the text's inerrancy and its status as scripture foreclose the possibility of revising the canonical text to bring it closer to any of the many vernacular forms of Arabic prevalent today. It is certainly possible to write a commentary on the original text in vernacular Arabic, but a wholesale revision of the text would be unthinkable. The Quran is considered perfect as it is, and any attempt to bring it closer to current vernacular forms of the same language would be considered a corruption of the text.
This isn't any different from having, say, a facing-page version of Hamlet with Shakespearean English on the verso and modern English on the recto. The modern English might help a beginner grasp the basic sense of Shakespeare's words, but the beauty of the language, the poetry, even the meaning of Hamlet qua Hamlet, inheres in the original. It would take some gumption to publish only the modern English rendition and pass it off as the Hamlet. Now add the fact that Hamlet isn't even scripture, and you can begin to appreciate the difficulty faced by someone trying to update the Quran to make it more intelligible to speakers of vernacular Arabic.
The only change that has been made to the Quran's written form since the establishment of the canonical version is the introduction of diacritical marks. The original text had very few diacritical marks. However, since their absence could lead to ambiguities in pronunciation (and hence in meaning), diacritics began to appear by the eighth century CE, i.e., within a few decades of the establishment of the canonical text.
The importance accorded in Islam to the recitation of the Quran in its original form has permitted standard Arabic to remain a lingua franca among the Muslim cultures of the Middle East and North Africa. Since modern standard Arabic is a descendant of classical Arabic, oratory, literature, and to some extent even news media remain largely mutually intelligible across the Arab world even when local dialects are not.
