The tree is scaled (climbed) from one branch to others. It is a progression tree rather than an equanimity tree. For example, a practitioner that can be still and has a healthy body may not need asana at all, very little asana, or specific asana.
As far as pranayama is concerned I don’t teach it in Savasana. I do teach it in either a prone or seated posture but the prone posture should not be confused with Savasana.
Pranayama done with the “aim of self healing” still mandates the movement of prana in the physical body. Therefore the position of the student is imperative (when moving prana). This isn’t the same as breathing nor is it the only breath work. So it is not inappropriate to do certain breath work without regard for the position (read:alignment) of the physical body. It is for this reason that supine pranayama is available - so that the student who cannot sit with alignment can have the proper position for directing prana safely.
Simply because the student’s “aim” is self-healing that does not mean their aim is true (read: accurate). Intention is certainly a prime mover but the most well intentioned practitioners have still done damage to their nervous system.
Relative to alignment and “asserting” there are some who need x-rays for such things. And let me be clear: an x-ray (or MRI) can be a huge advantage, even a “must”. However, most skilled, alignment-based teachers have learned to see the spinal alignment for pranayama with the naked eye. It is the art of superimposing the pose over the pose.