Why is a “Nazir” not allowed to drink wine?
If the reason is for him being sober, then why the prohibition on haircuts or the injunction against being impure?
Moreover, in the pasuk it says “מִיַּיִן וְשֵׁכָר יַזִּיר” which can be explained as "wine or any other intoxicating material" is explained by Rashi as grape juice or wine specifically, so other intoxicating beverages are allowed.
If it has more to do with purity and impurity rituals, why only grapes and not other intoxicating beverages?
There is a long article on the “reasons” for the “Nazir” not being allowed to drink wine and the other restrictions at the Yeshivat Har Etzion virtual beit hamedrash .
Ultimately any reasons we can think of do not approach the intent of Hashem and this is the only "answer" I have seen to the last question that you ask.
The article mentions many ideas of which I offer:
According to these commentaries (Rashi and Ibn Ezra), becoming a nazir means separation or abstinence, aimed at distancing the person from transgression. The nazir avoids drinking wine and brandy, which cause inebriation and may lead to sin. However, from the Ibn Ezra's explanation we see that there is more involved here than just keeping oneself from sin. There is also the element of acting "for the sake of God's service."
Rav Shimshon Refael Hirsch discusses this point: The avoidance of anything that is made from grapes will be a constant warning for him. As a nazir, he has a great mission – to repair his thoughts and his feelings. Therefore, he is obligated to maintain the clear head and equanimity required for this service.
The three prohibitions may be viewed as a progression:
Separation - Prohibition against wine
Holiness - Prohibition against ritual impurity
Separation and Holiness - Prohibition against haircuts
