I am somehow internally very attracted to the idea as also very optimistic that this might be done at some point
A few languages implement the idea.
What really matters is, does implementing a feature enable a programmer to create code that is simpler and easier to understand than without that feature ?, for the extensible grammar feature, the answer is clearly: no.
The reason is very simple, a program that uses that feature, requires the programmer to inspect and understand a dynamically defined grammar then mentally put together how that grammar applies to the problem the program as a whole is attempting to solve. That's a whole lot more work than dealing with a static grammar whose actions are (hopefully) clearly documented in the language definition.
IOW, extensible grammars result in programs that use undocumented constructs since their definition is found in only one place: the programs that defines them.
Extensible grammars are a bit like self-modifying code. They enable the programmer to do some rather fancy stuff but, they are rather detrimental to ease of understanding.
Academically, they are very interesting, in practice, they really aren't desirable in a program that is easy to understand and maintain. Not to mention that tracking down a bug resulting from a problem in the dynamically defined grammar can greatly increase the proliferation of the bald gene in the programmer's genetic pool.