The main reason is that the only accepted version of the Qur'an is one that is in Arabic, whereas this is not the case with the Hebrew Bible nor the Christian New Testament. For many Christians and Jews, scriptural texts written in English (or French, or German, or Swahili, what have you) are all just as authoritative as the original languages. Thanks to the Romanization of the Church under Constantine, Latin really took hold as the language of the texts of Christianity (earlier on, Greek was the primary language of scripture...but this, too, was more or less pushed out by the ascendency of Latin). The Second Vatican Council pushed Latin more to the background for the Catholic Church; even still, many denominations that had split off from the Catholic Church had already moved into using texts written in various vernaculars. (Even the Vulgate is a step in the direction of biblical texts written in a vernacular.) Hebrew has always held a special place in Judaism...although there are really more "Jewish" texts written in various dialects of Aramaic than there are texts in Hebrew (and many of the Hebrew texts exhibit Aramaic influence themselves).

Keep in mind too, the variance in mutual intelligibility between actually spoken Arabic of different regions and the Arabic of the Koran is also quite wide.

It could be loosely akin'd to saying much of Europe speaks "Romance", ignoring the wide intelligibility problems between each country's language, despite coming from a common root.

I'd dispute that Arabic is more dominant in Islam than Hebrew is for Judaism. Hebrew was the primary language of Jews in ancient times, and was used as a literary language after that. Sure, it was mostly in religious contexts, but this was people producing new Hebrew-language literary material, not just referring to Hebrew-language canonical literature. And, of course, Hebrew was a big enough ideological piece for it to be successfully revived as a natively spoken language, which is extremely rare (if it's happened in other cases, which is debatable (Cornish?), it's certainly the most successful example of it by far).

Since Jews have been a minority group pretty much everywhere when Hebrew hasn't been the primary language, it wouldn't really be expected for Judaism to bring Hebrew as a main language anywhere--it doesn't have the numbers the way Arabic did. But Jewish languages consistently have a noticeable level of Hebrew loans, and in many cases those loans passed to the local language.

Religion has no doubt been a big part in the Arab conquests. My point would be that it is scale and also perhaps the relative recentness of those conquests that explains the spread of Arabs and the Arab language. I do not see a reason to overcomplicate things by seeing religion - and specifically its reliance on the one language - as the prime mover here.

As you say Islam must have had a great galvanizing impact to unite the Arab tribes and make the conquests possible, but it coulr be argued that with a different religious language of Islam, the middle east would still be speaking Arab. That is a big IF of course.

As an aside I think we are pretty unsure about the state of Islam during the Arab conquests. Confirmed findings of qurans for example date - as far as I know - from after the time of the conquests. Using the Quran as a tool for language spread during this time may thus be problematic.