Not even those lived in the time of the Bible used biblical Hebrew.
One of main differences of Torah Hebrew and the Hebrew of Kutuvim is the style of language (I read that in a sefer, but can’t recall the source). Look at Megillat Ester, for example. It’s Hebrew is much closer to modern Hebrew than the Torah is to Modern Hebrew. The language of Hashem’s Torah is unique. The Hebrew of the Neviim is also unique, but Ketuvim was often written in the vernacular.