mmm...i am not so inclined to agree. if eating lunch, with silent receptive mind, consciousness converges on breathing. similarly, if walking with silent receptive mind, consciousness converges on breathing. if typing, with silent receptive mind, consciousness can converge on breathing. sitting back & reading, rolling the mouse, the mind converges with breathing
it may sound unusual to say, but, imo, 'placing' ones awareness on breathing is, imo, not really related to Anapanasati. imo, such a phrase is non-sequitur in respect to Buddha-Dhamma because the establishment of mindfulness is maintaining the mind free from craving. There is only one essential practise in supramundane Buddhism, which is abandoning craving, attachment, liking & disliking.
Let us take the later stages of Anapanasti as examples. Can placing ones awareness on rapture be practised? Can placing ones awareness on the mind with anger be practised? Of course not.
The breathing steps are the same. They do not manifest from "placing ones awareness on the breathing". Imo, placing ones awareness on the breathing is hatha-yoga rather than Buddha's mindfulness practise.
Naturally, we do not have the accept what i am saying. It is just an opinion. Instead, we need to stop placing our awareness on the breathing until the mind becomes aware of the breathing without placing its awareness on the breathing. Then was can verify for ourselves that we do not need to place our awareness on the breathing for the mind to become aware of the breathing.
Further, when the mind becomes aware of the breathing without placing its awareness on the breathing, we can continue to not place awareness on the breathing even though the mind become more & more aware of the breathing.
Imo, this is the Buddha's training, namely, not attaching or clinging to anything. Placing ones awareness on the breathing is, arguably, a form of clinging. And no! It is not a skilful means. It is simply training wheels for beginners. But in real practise where: 'He trains himself', I suggest the mind deliberately does not place attention on the breathing. Instead, the mind remains free & void. When the mind remains free & void, the breathing can certainly come to the mind & the mind can converge with the breathing.
It seems we agree. 'Anapanasati' is 'mindfulness with breathing' (rather than mindfulness 'of' breathing).