halacha - Why can people write Torah sheBal Peh nowadays?

This is a follow up to: Why was Torah SheBe'Al Peh not allowed to be written?.

The Gemara in Temurah 14b states that one may not write Torah sheBal Peh. It then states an exception that was made so that Torah would not be forgotten.

ותנא דבי רבי ישמעאל: כתוב לך את הדברים האלה - אלה אתה כותב, אבל אין אתה כותב הלכות! אמרי: דלמא מילתא חדתא שאני; דהא רבי יוחנן ור"ל מעייני בסיפרא דאגדתא בשבתא, ודרשי הכי: +תהלים קי"ט+ עת לעשות לה' הפרו תורתך, אמרי: מוטב תיעקר תורה, ואל תשתכח תורה מישראל.

Similarly, the Mishna and Gemara were only able to be written because otherwise Torah would have been forgotten from Israel. The general prohibition seemed to have been kept for other writings. (Even after the Gemara was written, the Geonim refrained from writing other works.) Yet what allows any work of Torah to be written nowadays? Not every work is preventing "Torah from being forgotten from Israel"!

Answer

There is a discussion of this topic here. The author there brings the gemara (Gittin 60a) regarding Chazal's exeptions to the rule of not writing down Torah Shebaal Peh and fragments of Torah Shebiksav based on "עת לעשות לה' הפרו תורתך", then the dispute between poskim:

We see that in order to facilitate Torah learning, Chazal permitted the writing of the Oral Torah and parts of the books of the Written Torah. To what extent did they override the original prohibition?

This is a dispute among early poskim, some contending that it is permitted to write only as much as is necessary to prevent Torah from being forgotten. According to this opinion, it is prohibited to write or print even tefillos that include pasukim that are not intended for learning Torah (Rif and Milchemes Hashem, Shabbos Chapter 16). This opinion also prohibits translating Tanach into any language other than the original Aramaic Targum because proper translations constitute Torah She’ba’al Peh. In addition, this opinion prohibits the printing of a parsha of Chumash in order to teach Torah, since one could write or print the entire sefer (Rambam, Hilchos Sefer Torah 7:14; Shulchan Aruch, Yoreh Deah 283:2). Other poskim permit the writing of any Torah that one uses to learn. Thus, they permit writing a single parsha in order to teach Torah (Taz 283:1; Shach 283:3) and the translating of Tanach into any language. These poskim rally support to their opinion from the fact that Rav Saadya Gaon wrote sefarim in Arabic, including commentaries on Tanach (Ran, Shabbos Chapter 16).

Both opinions agree that it is prohibited to publish translations of Tanach that will not be used to spread Torah knowledge (Ran, Shabbos Chapter 16).