There is certainly an element of wheel re-invention in first principles thinking, but acquiring maker's knowledge seems like a more rewarding endeavour than acquiring only user's knowledge.
This process of creating new languages/jargon has a name in Computer Science: Meta-linguistic abstraction [1], and so the value of Philosophy (to me) is in the first paragraph of the Wikipedia article:
>metalinguistic abstraction is the process of solving complex problems by creating a new language or vocabulary to better understand the problem space.
And so this I find it fascinating when you say that...
>there are certain symmetry groups that seem to apply everywhere we look
Because your meta-language for talking about your experiences is the language of symmetry groups.
Post-structuralism (and all Philosophy, really) is merely an attempt to escape the reductionist nature of that sort of language-centric thinking - it's an attempt to drag us out of the cave of Logocentrism [2]. Mathematics is only up to isomorphism - there's nothing in the symbolic denotation without the human connotation, so if structuralism is about symmetry (equalities) , post-structuralism is about asymmetry (inequalities).
[1] https://en.wikipedia.org/wiki/Metalinguistic_abstraction
To take a specific example, I'm curious what post-structuralism actually means as applied to the structure I was trying to refer to - there are certain symmetry groups that seem to apply everywhere we look, but the actual structure is itself isn't a symbolic concept in the same way the standard model is.