Panini's grammar is closest to an instance of a Post canonical system. It is basically a set of general rewriting rules, with features going beyond BNF in power.

This is for pretty much the same reason that the grammatical formalisms modern linguists use also go beyond BNF. Linguists are interested in issues of grammaticality that actually do need context (such as subject-verb agreement) and so obviously context-free grammars can't do the whole job!

(For a programming example, you can see type correctness as a case of how well-formedness of programs depends on context -- whether a variable can be used in an expression depends on its type.)