What is the shortest distances between two points? A straight line. I calculate the solution to that problem. I don't design it. What's the best way to travel between two points? Do I take a car or plane? Which is cheaper, faster, or more comfortable? I can't calculate a solution because the problem is to complex. Instead I design the solution to the problem. That is the fundamental difference between design and calculation.
Whenever you use the word "design" you are operating in a zone where humans have no foundational optimization theory. You are guessing, using your instincts, your common sense and your gut to find solutions for the problem. It's unlikely you'll hit the most optimal solution, but you can very likely arrive at a "good" solution.
If you squint, Category theory looks to fill this gap for designing programs. Depending on how you look at it, category theory looks like a fundamental theory on how to organize code. It can be thought of as a fundamental theory on abstraction or a fundamental theory on interfaces.
Maybe another way to put it is that the concept of interfaces are the maxwells equations of software..
Even turing machines/lambda caculus seem oddly specific let alone lisp. If we want something fundamental and general I think Category theory is it.
My guess is, if the advancement of computer science was allowed to play out for centuries and we got rid of all the historical baggage, some form of category theory would lie at the heart of it all.