To be a mathematician computer programmer, you don’t have to use the Church-Turing mental framework all the time. Sometimes it’s useful and sometimes not.
Of course you don't. I never said you did. In fact I would argue you never think about this isomorphism 99% of the time.
I'm just saying that a big portion of the math doesn't describe the real world implementation details.
As I said the Church side of the theory doesn't have a real world machine equivalent. We have machines that move things and save things but we don't have a physical machine that represents the concept of a function call. What we instead have is a Turing machine that emulates a function call, not a true simulation of it.
