The brrring reduces the pressure and tension required to make a noise. If your lips are getting numb, it may be because they are brring too fast. It should be quite slow, so you can almost see them bouncing up and down. Kinda funny to watch
Anyway, the benefit of reducing the pressure required is that you can work on your technique in a very comfortable way. Then you can move that technique back into your full voice. In this way you can discover effective vocal configurations with much less risk of introducing tension.
Cloudwind, how does that exercise counter the lip trill? Is it because lip trill encourages pop style singing but that exercise encourages classical style singing?