Full disclosure: my mother runs a practice in NYC and implements Buteyko a lot with patients. It’s called HappyMyo and I helped her set up the website.
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I think Buteyko suffers from a marketing problem wherein it sounds really “eastern medicine”. I think it actually can be super beneficial to people, assuming they have the patience and discipline to commit to it for many months. It’s not easy and I think the success rate is so high because the people that seek it out are pretty determined.
I strongly encourage people research myofunctional therapy also if you snore/have sleep issues or find yourself out of breath often. It’s like physical therapy for your airway where you do lots of exercises regularly over months. I’m not even trying to advertise here, just trying to spread the word in case it helps someone.
links: Assorted research papers - https://happymyo.com/2024/02/11/research-papers-on-omt/
A sample of what the exercises look like, I am not affiliated with this site and these are the ones without props - https://www.singhealth.com.sg/tests-procedures/myofunctional...