I think I can relate to some of Ashtangas concerns. It is very difficult to someone to get rid of the self view (IMO and experience) using just the breath. We hardly relate to ourselves as the breath. So how would seeing the breath help- considering that the self view is very strong and that the symbolic nature of the breath as representing everything else may be difficult to perceive.
In my experience and knowledge people get rid of the self view (through meditation) commonly in these instances:
1) seeing that there is no self while doing walking meditation (no doer)
2) while doing 'foulness of the body' contemplation
3) while seeing that existence consists of packets of impermanent phenomena- bare awareness (ie- how can there by a continuous thing as a self)
4) when seeing that those packets of sensory stimuli are causally arisen and have no substance in themselves. for example the eye and the visual object give rise to the thought perceiving it, without the eye and the visual object there would be no such thought- hence everything that we consider the mind arise from something else prior to it)- hence no independantly existing 'self'
There are vipassana techniques aimed just at this in the Theravada tradition. I respect Anapanasati but I suspect that it is a good technique for those who are quite intelligent to see the parallels and have good samadhi and good sati to determine fine details while breathing. Different strokes for different folks. We dont have to be attached to any particular method- just do what gets the job done. Theravadin vipassana methods can get into non-conceptual emptiness just as well