Very interesting. I feel like the very concept of a grammar is only a model we cast on language to make it easier to deal with. Langage is pretty free and can work without it. Grammar feels to me like a normalization "by contract". We normalize, then study the normalization tool itself without being aware it is an artefact. We model the model, give it free parameters, randomness, serendipity to make it accomodate reality and its endless string of special cases. We even try to separate meaning from experience.

This all feels more like a network of relations and probabilities of coocurrence of various (free?) orders. I followed your link and I strongly feel the suffix "grammar" is the real burden here. We're trying to put structure on what is actually creating it.