Why do Moses' children play such a small role in the Torah? There is barely mention of them. It would seem his offspring would be of the utmost importance in the Torah narrative and would carry the torch after Moses' death. But it's his brother, Aaron that takes center stage on most occasions.
Several of the commentators address the absence of Moshe's children from an enigmatic snippet where they would appear to belong (B'midbar 3):
וְאֵלֶּה תּוֹלְדֹת אַהֲרֹן וּמֹשֶׁה בְּיוֹם דִּבֶּר ה' אֶת מֹשֶׁה בְּהַר סִינָי. וְאֵלֶּה שְׁמוֹת בְּנֵי אַהֲרֹן הַבְּכוֹר נָדָב וַאֲבִיהוּא אֶלְעָזָר וְאִיתָמָר. אֵלֶּה שְׁמוֹת בְּנֵי אַהֲרֹן הַכֹּהֲנִים הַמְּשֻׁחִים אֲשֶׁר מִלֵּא יָדָם לְכַהֵן
The Torah, sounding as if it is going to tell about the offspring/products of both brothers Aharon and Moshe, only goes into the family of Aharon - who they were and what became of them.
There, Shadal says that the Torah was deliberately making brief mention of Moshe's children to show that they neither sought nor deserved the grandeur that was assigned to the kohanim who descended from Aharon.
ואמר "ואלה תולדות אהרן ומשה..." ולא הזכיר תולדות משה להודיע כי גם משה העמיד תולדות. אלא שלא רצה ה' להקדישם להיות כהנים, ולא חלק להם שום גדולה, ולהגיד שלא היה משה מבקש גדולה לעצמו.
This counteracts the premise that his children would be of utmost importance, for that was simply not their place in the bureaucracy.
Rashi and others following his talmudic suit (e.g. Ramban and especially N'tziv) unask the question by saying that the sons of Aharon were the exclusive intellectual heirs to Moshe, so the Torah really didn't leave out his tolados at all.
While not specifically about Moshe, perhaps the following Talmudic passage is relevant:
ומפני מה אין מצויין ת"ח לצאת ת"ח מבניהן אמר רב יוסף שלא יאמרו תורה ירושה היא להם רב ששת בריה דרב אידי אומר כדי שלא יתגדרו על הצבור מר זוטרא אומר מפני שהן מתגברין על הצבור רב אשי אומר משום דקרו לאינשי חמרי רבינא אומר שאין מברכין בתורה תחלה
And why is it not usual for scholars to give birth to sons who are scholars? — Said R. Joseph, That it might not be maintained, The Torah is their legacy. R. Shisha, the son of R. Idi, said: That they should not be arrogant towards the community. Mar Zutra said: Because they act high-handedly against the community. R. Ashi said: Because they call people asses. Rabina said: Because they do not first utter a blessing over the Torah. (Soncino translation)
Several of these reasons could have been applicable had Moshe's children had important roles. Indeed, Moshe was already accused by Korach of taking too much power for himself and his family.
See also this article from Tradition in 1988 by Dr. Irving N. Levitz, studying the general issue of being a child of a rabbi.
Chassam Soffer addressed this twice and offered two different reasons based off medrashim why Moshe's sons did not succeed him.
In a tshuva seen here he suggests they were just as worthy as Yehoshua, but Yehoshua became leader specifically because he set up the chairs in the Beis Medrash.
אע"כ הי' הבנים ראוי' לכך והקב"ה לא אמר שיהושע יותר הגון לכך אלא שסידר הספסלי' ואת המחצלאו'
In his drashos seen here s.v. ki, he suggests, again based off a medrash and Rashi in parshas Yisro, that Moshe Rabeinu's sons were actually unworthy as he neglected them while caring for the community at large.
הוא לא השגיח על על בניו מטרדת הציבור כפירש׳י, יתרו