A tree is a graph so I’m not sure I understand your idea. But, at the end of the day, the point of the tree is just to represent the relationships between the tokens. There IS a relationship. As long as your theory represents that as precisely and with as much predictive power as trad linguistics, it doesn’t really matter how.

I’m also not sure why you are talking about why natural languages are not different from other ones. That is what I’m saying, it’s the reason behind the comment that all parsing works the same way.