I insist on specification and not just file format
Actually, the file format of DNG is the same as that of most raw files, namely TIFF.
that would mean in my example they would have to use matrix-based profiles
They would have to attach the matrixes for the primary conversion, and now they could attach the profiles as well to "fine tune" the result of the primary conversion.
Furthermore, they could include all proprietory information as well, but those would remain proprietory.
Note, that the proprietory information is necessary for example to figure out in-camera settings, like contrast, picture style, and some other features. However, the color reproduction is based usually on the specific knowledge of the sensor (spectral characteristics), i.e. it is hard-wired in the programs.
Which many people including you have argued, and Adobe have implicitly half admitted with their latest DNG specification, are not totally capable of correctly converting the raw data to RGB color information for all different illuminants
1. The new features (i.e. profiling) are a huge enhancement. I re-did a few conversions and am surprized by the huge difference (positive), using the new profiles, created by Adobe. I am very pleased by this.
2. Notwithstanding my pleasure with the new profiles, the basic problem remains: that the matrix conversion limits what a program can do. I do not know if and how much this limitation is regarding specific cameras. I would expect that Adobe investigated this question, but I guess we won't see the result.
mainly due, as I understand it, to non-linear sensor response
Caution with this. There are two totally different meanings of "non-linearity" in conjunction with sensors. The issue at hand is the spectral response, and this aspect can be ignored here, for nothing will change that in the near future.