Tefillin, for being a quite fundamental part of Judaism, and which were apparently worn all day long in Ancient Israel, are never mentioned in Nach. How would these sacred objects, which are quite noticeable, and (at the time) a significant part of the daily attire are not be mentioned anywhere in Nach?
There are two assertions that were made here that need to be assessed:
Tefillin, for being a quite fundamental part of Judaism, and which were  apparently worn all day long in Ancient Israel, are never mentioned in Nach. How would these sacred objects,  which are quite noticeable, and (at the time) a significant part of the daily attire are not be mentioned anywhere in Nach?
- The statement that Tefillin were always worn all day is only stated in regards to Talmudic times. Regarding pre-Talmudic times (i.e. during Nach), I have not heard that this was also the case and did not find any sources that said one way or the other (see below).
- The statement that the Tefillin were obvious and visible was not necessarily true in Talmudic or pre-Talmudic times.
To answer these questions, it's important to look at the sources of wearing tefillin during the whole day, who did it, and how obvious was its appearance.
Sources for wearing Tefillin the entire day
There are multiple sources for wearing Tefillin all day in Talmudic times. This practice is evident of R' Yochanan ben Zakkai (Sukkah 28a) and R' Zeira (Megillah 28a) of that which is more clearly stated in Menachos 36a:
ועד מתי מניחן עד שתשקע החמה רבי יעקב אומר עד שתכלה רגל מן השוק וחכמים אומרים עד זמן שינה ומודים חכמים לר' יעקב שאם חלצן לצאת לבית הכסא או ליכנס לבית המרחץ ושקעה חמה שוב אינו חוזר ומניח
And until when does one wear them? Until the sun sets. Rabbi Ya’akov says: Until traffic in the marketplace ceases. And the Rabbis say: Until the time of sleep. And the Rabbis concede to Rabbi Ya’akov that if one removed them to go out to the bathroom or to enter the bathhouse and the sun set, one does not don them again.
The Rambam (Hilchos Stam 4:25) brings down this idea and says:
אָמְרוּ עָלָיו עַל רַב תַּלְמִידוֹ שֶׁל רַבֵּנוּ הַקָּדוֹשׁ שֶׁכָּל יָמָיו לֹא רָאוּהוּ שֶׁהָלַךְ אַרְבַּע אַמּוֹת בְּלֹא תּוֹרָה אוֹ בְּלֹא צִיצִית אוֹ בְּלֹא תְּפִלִּין:
It is said of Rav, the disciple of our Sainted Teacher (R. Judah, the Prince), that throughout his life no one saw him, without Torah, Tzitzis (fringes on his garments) or phylacteries.
Sources for not wearing Tefillin all day
However, wearing Tefillin all day appears that this was not necessarily the case even for some of Chazal (let alone the majority of the population). In Yerushalmi Berachos 14a we see:
ר' ינאי היה לובשן אחר חולייו ג' ימים לומר שהחולי ממרק מה טעם (תהילים ק״ג:ג׳) הסולח לכל עוניכי הרופא לכל תחלואיכי רבן יוחנן בן זכאי לא הוון תפילוי זעין מיניה לא בקייטא ולא בסיתוא וכך נהג ר' אליעזר תלמידו אחריו ר' יוחנן בסיתוא דהוה חזיק רישיה הוה לביש תרויהון ברם בקייטא דלא הוה חזיק רישיה לא הוה לביש אלא דאדרעיה.
R' Yannai would wear tefillin three days after recovering from an illness, because an illness purges [one of sin]. Why? "He forgives all your sins, heals all your diseases." (Tehillim 103:3). Rabbi Yochanan ben Zakkai wouldn't remove his arm tefillin in the summer or the winter. In the winter, when R' Yochanan would [wrap his turban], he would wear both Tefillin. However, in the summer, when R' Yochanan was not [wrap his turban, because of the heat (Pnei Moshe on Yerushalmi)], he would only wear the arm Tefillin.
We see that R' Yannai seems to only have worn Tefillin after a recovery, and R' Yochanan and R' Yochanan ben Zakkai would at least sometimes only wear the shel yad. The above only applied to Chazal themselves, what about the rest of the population?
Tosfos on Shabbos 49a brings in (via the story of Elisha Ba'al Knafayim) two big reasons why Tefillin was treatly lightly during Chazal and even now. (1) Because they couldn't maintain a clean guf enough to constantly wear them and (2) There were deceivers that would wear tefillin all day only because they wanted to be considered upright so that they could then deceive people.
Tosfos brings a Gemara in Shabbos 130a, which says:
תניא רבי שמעון בן אלעזר אומר כל מצוה שמסרו ישראל עצמן עליהם למיתה בשעת גזרת המלכות כגון עבודה זרה ומילה עדיין היא מוחזקת בידם וכל מצוה שלא מסרו ישראל עצמן עליה למיתה בשעת גזרת המלכות כגון תפילין עדיין היא מרופה בידם
It was taught in a baraita that Rabbi Shimon ben Elazar says in praise of the observance of the mitzva of circumcision: Any mitzva for which the Jews sacrificed their lives at the time of the decrees of the wicked empire, such as the prohibition of idolatry and the mitzva of circumcision, is still steadfastly observed. And any mitzva for which the Jews did not sacrifice their lives at the time of the decrees of the wicked empire, such as phylacteries, is still casually observed, meaning that they are not as careful in its fulfillment as they should be.
Where he mentions that the mitzvah was "רפויה בידם" as we see from that source, in addition to that which was on Rosh Hashanah 17a:
פושעי ישראל בגופן מאי ניהו אמר רב קרקפתא דלא מנח תפלין פושעי אומות העולם בגופן אמר רב בעבירה
The Gemara asks: The rebellious Jews who have sinned with their bodies, who are they? Rav said: This is referring to the skull that did not ever don phylacteries. The Gemara asks further: The rebellious ones of the nations of the world who sin with their bodies, who are they? Rav said: They are those who engage in the sin, i.e., forbidden sexual relations.
(And he brings in a Midrash Shocher Tov to show the deceivers that would abuse their superficiality)
Based on all of the above, it would seem to be that it was possible there was likely many Chachomim wearing Tefillin (but not all), and much less of the general population because of Tosfos' two reasons.
L'halachah, the Shulchan Aruch (OC 37:2) discusses the mitzvah during the day:
מצותן להיותם עליו כל היום אבל מפני שצריכי' גוף נקי שלא יפיח בהם ושלא יסיח דעתו מהם ואין כל אדם יכול ליזהר בהם נהגו שלא להניחם כל היום ומ"מ צריך כל אדם ליזהר בהם להיותם עליו בשעת ק"ש ותפלה:
It is a Mitzvah to have them [tefillin] on all day, but because they [tefillin] need a clean body [meaning that] he does not pass gas, and [further require] that one not distract his mind from them, and not every person is able to be careful with them, the practice is not to wear them all day. Nevertheless everyone needs to be careful with them when they are on during the reciting of Shema and Tefilah [aka Shemoneh Esreh] [because we concentrate on holy things at those times anyway].
The Biur Halachah brings the Pri Megadim about whether the Torah itself requires is to be wearing Tefillin all day or not, and even talks about the idea of even wearing just the Shel Yad (like we said by R' Yochanan), that I think says some nice things regarding what we said above:
עיין בפמ"ג שמסתפק אם מן התורה חייב כל היום או מן התורה די ברגע אחד שמניח ומדרבנן כל היום ובטלוה עכשיו שאין לנו גוף נקי ומסיק דעיקרן של דברים דאם לא הניח יום א' כלל לתפילין ביטל מ"ע ובהניח רגע עליו קיים המצוה אבל מצוה מן המובחר מן התורה להיותן עליו כל היום וכו' עיין שם. ובספר ישועות יעקב פסק דמן התורה מצותן כל היום עיין שם.
See in the Pri Megadim, where he is uncertain about whether wearing Tefillin all day is an obligation from the Torah, or if it's just enough for just a moment, and that it's d'rabbanan during the whole day since now we don't have a guf naki. He concludes that one can fulfill the mitzvah by just wearing them for a moment. The sefer Yeshuas Yaakov says that it's an actual mitzvah from the Torah.
Whether Tefillin are noticeable
While I don't know what was worn pre-Talmudic times, it is commonly understood that in Talmudic times (as in Bavel) and for many centuries later, the common practice was to wear robes and a turban (for example, I've seen Egyptian pictures from pre-Talmudic times, that show people wearing things like sock hats). It would seem that according to the clothing of the time, the Tefillin may commonly have been covered, both on the head and the arm (that is, as we saw in the case of R' Yochanan, above, who would only wear the shel yad in the summer. Presumably, he would not have worn his Tefillin over his turban because of chatzitzah).
It appears to me that it's possible:
- The Jewish people were not always wearing Tefillin (or even just the shel yad Tefillin) necessarily all of the time
- The clothing and way the Tefillin were worn could very easily have covered them up if they were in fact being worn all of the time.
P.S. This is what I found. I'm hoping that if I made any mistakes, I can be corrected, and that this can be a catalyst for some more discussion and bringing down of some more sources.