[tel]

Outside the topic of admittedly really cool delcont stuff:

The way you refer to the value and the CPS'd value as the same is by referring to their effects in stack machine semantics as the same. This makes your intuition non-transferrable to other semantics (lacking a clear CS example off the top of my head, I'll just throw out the usual trick of asking: does this work the same on a GPU? I'm confident there's a Yoneda analogue there).

Studying CT is completely extra-curricular as far as I'm concerned and I could never recommend it as a way to implement or use CPS, but understanding, for certain rather aggressive values of "understand" I feel comes from nearly no other pathway. It's entirely too beautiful and simple (for certain mathematical values of "simple") to escape.

Also the commutative diagrams are pretty much exactly the same as the chemistry ones you're talking about. Both are just ways of writing down systems of equations that are quite hairy to write out "long form".