1. Teaching the beginning concept of lip vibration, embouchure formation, air.
2. The beginning concept of lip flexibility
3. The overall concept of centering pitches from mouthpiece to Horn. Even centering lines...this trains both ear and gives a better sense of relaxation and "center" for an overly "tight"/"sharp" player.
Other than that, me as a pro, I don't spend too much time on buzzing other than to utilize no. 3 as a supplemental fix. I may warmup up on long tones from horn to mouthpiece and mouthpiece to horn aiming for pitch center on mouthpiece then horn.
But I found mouthpiece buzzing just for the sake of doing it, does nothing for my horn playing. For beginners, there is more benefits to buzzing melodies and specific pitches. I try to tell people to not just do random sirens, it doesn't do much. It may loosen the lips but does nothing for the ear and centering on the horn if they are not hearing the pitches to slur to first.