Agreed that it gets confusing. That's a piece of why I'm unable to give you a solid answer. This isn't my area of expertise.
Here is what I can tell you confidently:
The original plan was to provide an ICC profile that approximates PQ as best as we could. But it wasn't enough. So the proposal was to force the profile name to be a special string. When a PNG decoder saw that name, it would ignore the ICC profile and do actual PQ.
Possibly more context (I just found this) from Apple. I'm not sure of date: https://www.color.org/hdr/02-Luke_Wallis.pdf
Slide 29:
"HDR parametric transfer functions not in ICC spec
Parametric 3D tone mapping functions not in ICC spec
- Neither can be approximated by 1-D or 3-D LUTs"
I'm not sure why they cannot be approximated by LUT. Maybe because of the inversion problem?
Here is what I can tell you confidently: The original plan was to provide an ICC profile that approximates PQ as best as we could. But it wasn't enough. So the proposal was to force the profile name to be a special string. When a PNG decoder saw that name, it would ignore the ICC profile and do actual PQ.
Here is that original proposal: https://w3c.github.io/png-hdr-pq/
Possibly more context (I just found this) from Apple. I'm not sure of date: https://www.color.org/hdr/02-Luke_Wallis.pdf Slide 29: "HDR parametric transfer functions not in ICC spec Parametric 3D tone mapping functions not in ICC spec - Neither can be approximated by 1-D or 3-D LUTs"
I'm not sure why they cannot be approximated by LUT. Maybe because of the inversion problem?