Anyway, I think what C++ would need is its own "BLAS C++ Standard Interface” for low-level functionality. This
can be supported by simple reference implementations or sophisticated high-performance implementations. But
we would have a common ground on which one can build high-level C++ libraries.

I agree, but there is no std type/concept for a matrix. At this stage, it is impossible for developers of linear algebra to write libraries in C++ since their users have to use the underlying library for their applications. With the bindings, we have tried to suggest such a common ground. I once (many years ago) started to build a library from the bindings, but gave up because of time constraints …