The problem with representing processes with grammars is that you can represent pretty much any process with a grammar, right up to the level of Turing machines and the Lambda calculus etc. The question is, always: how useful is it to do this in practice?

With language, we assume that there is some sort of underlying structure that can best be modelled as a grammar (well, some of us do). In simple terms, we assume that natural language already has a grammar so that we can hope to eventually reconstruct it somehow- either by hand, or by automated inference etc.

Unfortunately, in practice every effort to do that sort of thing undertaken since Chomsky's Syntactic Structure was published in 1957, has been met with failure and even theoretically the outlook is bleak (see Gold's result and a ton of bibliography on inductive inference before and after it).

In short, the problem is not that it's hard to convince ourselves that there are processes in nature that are best modelled using hierachical representations, like grammars. The problem is that even armed with those representations we've so far proven incapable, with all our science and technology, to accurately use such representations to fully model those processes.

Basically, our current situation regarding the modelling of complex hierarchical processes is like being given the key to heaven, but no map to the damned gates.