A good point, and I would add that if you explore even deeper, you will find that what is usually referred to as yoga in the west is already itself a western ad

A good point, and I would add that if you explore even deeper, you will find that what is usually referred to as yoga in the west is already itself a western adaptation of a very small part of yoga which aims to improve physical (rather than mental) well-being. You don't see many people at gym yoga classes singing prayers or trying to control their dreams :)