The vibrations coming out of the mouth also come back into the ears to create a feedback loop that further stimulates the nervous system and helps to focus the mind. Proper singing and LOUD vocalization make people breathe deeply by bringing the diaphragm into play to forcefully press air out of the lungs. These observations come from years of testing in the context of university music teaching. During those years I met with all my music students from freshmen to Ph.D. candidates twice weekly for two-hour sessions. The first 10-15 minutes of every meeting focused on elephant swinging and singing for the purposes of deep breathing, physical and mental relaxation, and tuning.
Adults have plenty of outlets for making loud sounds.
If you're looking for a loud adult experience, just attend any professional, college, or high school sports event. Try an Italian, or Greek, or Mexican, or just about any wedding reception. Meditative chanting from the ancient eastern religious traditions incorporates but goes far beyond deep breathing, mechanical cleansing, and clearing the mind of its incessant chattering. The tuning is based on the principles of both physical and spiritual resonance and entrainment. And that is one of the most important arguments for supporting music performance in all our educational systems, especially K-12.