Our Gemara on Amud Beis records a discussion between Rabbi Shimon Bar Yochai and his students:
שָׁאֲלוּ תַּלְמִידָיו אֶת רַבִּי שִׁמְעוֹן בֶּן יוֹחַי נָזִיר טָהוֹר וּמְצוֹרָע מַהוּ שֶׁיְּגַלֵּחַ תִּגְלַחַת אַחַת וְעוֹלָה לוֹ לְכָאן וּלְכָאן אָמַר לָהֶן אֵינוֹ מְגַלֵּחַ
The students of Rabbi Shimon ben Yoḥai asked Rabbi Shimon ben Yoḥai: With regard to one who was a pure nazirite and a leper, what is the halakha concerning the possibility that he may shave one shaving and it will count for him both for this and for that? In other words, can it serve for his shaving of leprosy as well as for his naziriteship? He said to them: He may not shave once for both requirements.
אָמְרוּ לוֹ לָמָּה אָמַר לָהֶן אִילּוּ זֶה לְגַדֵּל וְזֶה לְגַדֵּל וְזֶה לְהַעֲבִיר וְזֶה לְהַעֲבִיר יָפֶה אַתֶּם אוֹמְרִים עַכְשָׁיו נָזִיר לְהַעֲבִיר וּמְצוֹרָע לְגַדֵּל
They said to him: Why not? He said to them: If the aim of both shavings were the same, this one to grow hair and that one to grow hair, or this one to remove hair and that one to remove hair, you would have spoken well. Now in actual fact the two shavings have different functions: A nazirite shaves to remove his hair, and a leper shaves to grow hair, so that he can shave again after the days of his counting.
We must analyze exactly why this is so. After all, if the hair is cut, so be it – and the requirement ought to be adequately fulfilled. Before we answer this question it is important to note that. The idiom, “ שָׁאֲלוּ תַּלְמִידָיו אֶת רַבִּי שִׁמְעוֹן בֶּן יוֹחַי “ “The students of Rabbi Shimon ben Yoḥai asked” throughout Shas invariably involves a philosophical question. For example, Megillah (12a) where Rabbi Shimon’s students ask why the Jews of Haman and Mordechai’s time were deserving of annihilation. Or, Niddah (31b) where the students asked why does a Yoledes (woman who gave birth) bring a sin offering when there was no overt commission of sin? Or Yoma (76a) when the students queried as to why the Manna did not come down in “Costco-like”, economy-size bundles to last an entire year, instead of a daily portion?”
Given this idiomatic pattern, it is highly likely that here too the question being asked was not halakhic as much as hashkafic. I find in a contemporary Sefer (Ohr Chanah, Rav Zundel Kroizer (1923-2014) a meaningful explanation. The function of shaving for the Metzora is at opposite ends to the shaving of the Nazir. The Nazir’s hair is considered a “crown” and is offered as part of the sacrifice (Numbers 6:7 and 18.). The shaving represents a demarcation from a holy state to a mundane state, and the older holy hair must be shaved, sanctified, and not mixed with the new hair which is profane. However, the Metzora shaves his hair to purify himself from his old ways and sins that have been encased in his hair (see Psychology of the Daf Nazir 9, where we saw that psychological trauma is recorded in the hair.)
Therefore, Rabbi Shimon and his students were discussing a philosophical point that emerged from the halakhic truth that these two rituals are not combined.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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