Most yoga classes that I know of are heavily dependent on asana, including my own. I’m aware though there are yoga schools that aren’t so closely tied into asana and include a wider variety of yoga practices and exercises in their program, which I applaud. I want to quickly affirm here that I find nothing wrong with modern yoga’s asana-heavy practice. I believe that such an emphasis is entirely appropriate at this time for Western practitioners, though not to the complete exclusion of breathing practice.
I’ve been teaching 10-15 minutes breathing practice at the end of every one of my classes, beginning and intermediate, for at least 25 years. The fact is that pranayama (along with meditation) was the core practice of Hatha Yoga for its thousands of years of evolution prior to the 20th century. Asana, though it gained in importance after about 1450 and the appearance of the Hatha Yoga Pradipika, was always considered a preliminary practice, a set up for breathing and meditation. These were the practices that created the ultimate transformation.