There is nothing like a valid criterion to discriminate "natural" in languages. All human languages are praxeostratic, they result from the cumulation of practices through time. Some might be more or less blank slate founded through theoretical jump, but even burning the bridge doesn’t mean creation ex nihilo. I mean, the only thing that would not be "natural", would obviously be "supernatural", like if one pretend a language to be some divine creation and not result of human contingent existence.

And just because utterances can be more or less matched with recursive tree doesn’t mean there is an ontological absolute truth about language there. Even "language" refers to some vague abstraction. Just like the "it" in "it rains" mentioned in this discussion: no entity out there actually respond to "language".

At introspection level, I absolutely don’t interpret utterances like recursive tree. They are more like cues going through living graphs more or less already connected and being able to change topology on the go. Impermanence of interpretation results is the only constant.

Now it’s not to dismiss that some other people might feel like "Natural language IS structured as a recursive tree" is the only way. People have different perspective, different brains, different life experiences. One who dwell in aphantasia¹ don’t perceive the world the same way as people that have hyperphantasia². Different of course here doesn’t mean better/worst or superior/inferior.

¹ A word I discovered in some HN comment

² A word that I had never red before but just popped up in my mind as I was thinking about this sentence, but which is actually already is in use in literature apparently: https://en.wikipedia.org/wiki/Hyperphantasia