The deuterocanonical books were originally written in Greek (not Hebrew), because they were written after 400 BC, when most Jews spoke Greek, and not Hebrew (these were the Hellenistic Jews, or the Jews of the Diaspora).
Not so much. The Hellenization of the eastern Mediterranean dates from Alexander’s little adventure, and thus starts c.320 BC. At this time, the Jews still spoke
Hebrew predominantly, as is evident from the Hebraisms rampant in the LXX (the Septuagint), my favourite being in Genesis 6:14. Greek gradually pervaded the society, eventually becoming the language of international communication around the eastern Mediterranean, although its degree of influence upon everyday society is very difficult to ascertain at any given point. There is, for example, some argument regarding how fluent Paul was in Hebrew.
The Jewish Diaspora, BTW, happened in AD 70, when Vespasian retook Jerusalem and banished the Jewish people from their homeland. The Exile happened back in the early C6th BC, when many were taken to Babylon.
This is why the Septuagint (the Greek translation of the Hebrew Canon, prepared for the Library in Alexandria) obviously includes the deuterocanonical books
Not exactly. The Septuagint has no “canon”, strictly speaking, and exists in a variety of forms, but many of those include not just “deuterocanonical” books, but also “apocryphal” ones such as 3 and 4 Maccabees.
the Gospel of Matthew, which was said (by Josephus) to have been written in “the language of the Hebrews”
This was Papias and then Irenaeus, not Josephus.
Jerome never said that the deuterocanonical books were not valid. They were part of the Christian Canon of his time, and he never called them into question.
This is
utterly untrue, as is self-evident from the prefaces which he himself wrote in the Vulgate. Those are available in translation
here.
Since the deuterocanonical books were originally written in Greek
Actually, there is considerable argument regarding the original language of a few of them. Sirach, in particular, is now widely suspected to have been written in Hebrew first.
these books could, indeed, be translated into the KJV. And they were (as I have already pointed out in this thread).
This is true for some editions of the KJV, but they are separated off as “apocrypha”, and it is really not relevant, because the OP’s question regarded
why Protestants rejected them.