No, it doesn't. Category theory is not intrinsic to the development, use or explanation of this technique. Category theory is merely one possible framework for explaining why the technique works the way it does. That's an important distinction, and likewise it's not the most practical framework for understanding this technique by a long shot.

In particular, understanding why certain programming techniques are more performant than others virtually never requires the language and abstractions of category theory. Everything you're saying here is a further demonstration of the complaints others have voiced in this thread. Not because you're wrong - you're not wrong. Rather because it's just not the most practical way of understanding or leveraging most programming techniques, and it injects a significant amount of unnecessary abstraction and foreign mathematical terminology into discussion.

For what it's worth I have taken graduate math courses wholly and partly focused on category theory, so I have the background to follow what you're saying. It's essentially correct. But it's also obtuse and mostly inscrutable to other people. It reduces, rather than increases, the shared context software engineers leverage to understand each other. You can project a vast and magnificent theory of categories onto programming because it adheres to a variety of algebras, but at the end of the day it's just not clarifying anything further. Instead it's miring it in overcomplicated verbiage.

There's basically no reason for you to be explaining why a regular expression is faster than a for loop for this use case with the formalism of category theory, unless it's as an academic exercise just to show you can. Explaining this example with the language of functors and type spaces is like proving that Excel is Turing complete in order to explain how summing arbitrary rows in a column works.