Question: why did the gemara exclude Moshe because he is not a kohen, forcing the gemara to pose the question with respect to Aharon and then come up with a new answer – why not exclude Moshe on the basis of his being a relative, and m’meila we wouldn’t even have to raise the question about Aharon because the same reason obviously would apply? Why not kill two birds with one stone if you can?
We once mentioned (link - see hesber there) the chiddush of the Maharal (quoted by the Shev Shmaytza in his intro) that the principle of ger she’nisgayeir k’katan she’nolad does not apply to a forced geirus, which includes the geirus of mattan Torah since kafah aleihem har k’gigis. This is why in our parsha Bnei Yisrael were crying (as interpreted by Chazal) over the arayos that became prohibited. Even though m’doraysa a ger has fewer issurei arayos, as he is like a newborn severed from all his part familial relationships, this din did not apply to the geirus of mattan Torah.
Based on this, the Kotzker (see R’ Wahrman’s She’eiris Yosef here) suggests a brilliant explanation of the gemara in Zevachim. Aharon had Sinai held over his head – he was part of the forced geirus of mattan Torah. The rule of ger she'nisgayei k'katan she'nolad did not apply to him, and therefore his relationship with Miriam was not severed. Moshe, however, was on the mountain – his geirus was not forced. The din of l'katan she'nolad would apply in his case, and therefore the gemara needed to offer an alternate explanation as to why he could not treat Miriam’s tza’ra’as.
Two other points worth noting:
What’s the hesber for this chiddush of the Maharal? The Kli Chemdah in Parshas VaYigash explains that the concept of geirus means divorcing oneself from one’s previous allegiance to nation and family and joining a new people. Conceptually, it makes no sense when applied to geirus en masse of the Jewish people. We did not leave some other nation to become Klal Yisrael at mattan Torah; we were and always will be the Jewish nation. We simply affirmed our identity and relationship to the Avos. According to this approach, it is not the element of coercion which negated the din of ger she’nisgayeir k'katan she'nolad at mattan Torah; it’s the fact that the experience of mattan Torah was unique in occurring to the Jewish people. This same logic would apply to Moshe Rabeinu as well.
Secondly, the Chasam Sofer in his chiddushim and al haTorah (in last week’s parsha) writes that his whole life he wondered what the makor for this din of ger she’nisgayei k’katan shenolad is. The Meshech Chocha in Parshas VaEschanan has an answer. Bnei Yisrael were told to separate from their wives in preparation for mattan Torah. Immediately afterward, Hashem commanded, “Shuvo lachem l’ohaleichem,” allowing them to return to their previous marriages. Says the Meshech Chochma: what would happen if someone was married to a woman who is an ervah by Torah law but was permitted to a ben Noach? How could this person return to his wife who is now an issur arayos to him? It must be, says the Meshech Chochma, that the heter of “shuvo lachem l’ohaleichem” is mechadesh that ger she’nisgayeir k’katan shenolad and therefore issues of arayos are moot.
If the Maharal is right that the din of ger shenisgayeir k’katan she'nolad did not apply by mattan Torah, then the Meshech Chochma’s proof does not hold water.