What happened to Leviim as teachers?

Question

In the Torah it seems pretty clear that the Kohanim/Leviim were supposed to be the teachers and moral guides of Bnei Yisrael (e.g., Devarim 33:10):

יוֹרוּ מִשְׁפָּטֶיךָ לְיַעֲקֹב וְתוֹרָתְךָ לְיִשְׂרָאֵל יָשִׂימוּ קְטוֹרָה בְּאַפֶּךָ וְכָלִיל עַל־מִזְבְּחֶךָ׃

And Devarim 17:8:

"כִּי יִפָּלֵא מִמְּךָ דָבָר לַמִּשְׁפָּט ... וְקַמְתָּ וְעָלִיתָ אֶל־הַמָּקוֹם אֲשֶׁר יִבְחַר ה"א בּוֹ׃
וּבָאתָ אֶל־הַכֹּהֲנִים הַלְוִיִּם וְאֶל־הַשֹּׁפֵט אֲשֶׁר יִהְיֶה בַּיָּמִים הָהֵם וְדָרַשְׁתָּ וְהִגִּידוּ לְךָ אֵת דְּבַר הַמִּשְׁפָּט׃ "

Yet in the rest of Nach we don't see Leviim taking an active role in teaching/rebuking Bnei Yisrael; rather, this is left up to the Neviim (e.g., Yehoshua, Eliyahu, Elisha, Yeshayahu). Indeed, in Pirkei Avot 1:1, the Leviim are notably missing from the list of people who transmitted the Torah:

"משֶׁה קִבֵּל תּוֹרָה מִסִּינַי, וּמְסָרָהּ לִיהוֹשֻׁעַ, וִיהוֹשֻׁעַ לִזְקֵנִים, וּזְקֵנִים לִנְבִיאִים, וּנְבִיאִים מְסָרוּהָ לְאַנְשֵׁי כְנֶסֶת הַגְּדוֹלָה."

(And the one example of leadership from the Leviim that we have is the corrupt sons of Eli!)

So what happened to the Leviim?

Answer 1

According to the Rambam, Hilchot Shemita 13:13, anyone who decides to "set aside to serve God and minister unto Him and to instruct people at large in His just paths and righteous judgments" (13:12) is considered like a Levite:

Not only the tribe of Levi, but any one of the inhabitants of the world whose spirit generously motivates him and he understands with his wisdom to set himself aside and stand before God to serve Him and minister to Him and to know God, proceeding justly as God made him, removing from his neck the yoke of the many reckonings which people seek, he is sanctified as holy of holies. God will be His portion and heritage forever and will provide what is sufficient for him in this world like He provides for the priests and the Levites. And thus David declared [Psalms 16:5]: "God is the lot of my portion; You are my cup, You support my lot."

Answer 2

We greatly misunderstand the idea of the relation between the Kohanim and the Torah.

1. To understand the original connection between the two we need to understand the true reason for placing the Sanhedrin near the Mizbeah as Rashi in Shmos 21:

"ואלה המשפטים. ... ולמה נסמכה פרשת דינין לפרשת מזבח,
לומר לך שתשים סנהדרין אצל המזבח: (OV המקדש)

2. The answer is the verse in Yeshayah 2:3:

"וְהָלְכוּ עַמִּים רַבִּים וְאָמְרוּ לְכוּ וְנַעֲלֶה אֶל־הַר־ה'
אֶל־בֵּית אֱלֹקי יַעֲקֹב וְיֹרֵנוּ מִדְּרָכָיו וְנֵלְכָה בְּאֹרְחֹתָיו
כִּי מִצִּיּוֹן תֵּצֵא תוֹרָה וּדְבַר־ה' מִירוּשָׁלִָם׃

So clearly Zion here is the Temple (read Kohanim) and Torah is the Sanhedrin (where the Torah is ruled).

3. Now it's time to conciliate the two: the reason is that the Torah that comes from the Sanhedrin can only be "true" if it is influenced by the Ruach Hakodesh that comes from the Temple/Kohanim. In other words, the Torah of the Kohanim is not the "worded" Torah you expect to be listed in Avos, but the Ruach of the Torah that Kohanim possess out of their "higher" spiritual state (טהרה וקדושה).

4. So in times when the Mishkan/Temple plays the key role in the Jewish people, e.g. the wilderness, the First Temple, the role of the Kohanim (Moses, Aharon and his sons, the Prophets you mentioned) in the Torah was big.
   When the role was "secondary" (as of the 480 years from Moses to the first Temple or after the destruction of the Temples) Kohanim lost the source of their "Ruach Hakodesh" and therefore have no additional powers than a regular (Israeli) Talmid Chochom.