In my experience, different communities have different practices with regard to shaving. (Note that when I talk about "shaving" in this answer, I mean cutting the beard with a permitted shaving device. Not a straight razor which is forbidden.)
In general, Hasidic Jews (including teenagers) tend not to shave at all. My understanding is that this is for kabbalistic reasons. The result is that teenagers often have kind of scraggly beard. In more "litvish" communities, on the other hand, my experience is that married adult men tend to have beards (either trimmed or long) while unmarried yeshiva bochurim tend to shave regularly. I think this is more an instance of fitting in with community norms rather than based on any particular halachic or hashkafic reasoning (and this practice is less universal among litvish Jews than the practice of not shaving is among hasidic Jews). By the time a man reaches marriage age, his beard usually grows in much thicker and more evenly than that of a teenager.
In any case, your premise that hair grows faster after shaving is not true. This is a mistaken belief likely originating from the fact that recently shaved hair tends to feel thicker than hair that has been allowed to grow. From that article:
Hair expert Philip Kingsley recommends thinking of a bamboo cane: a long cane flexes easily, but the same cane cut short feels harder and tougher.
So if your goal is to grow a beard, shaving it isn't going to make it happen any faster.