And the RAM your computer is writing everything to is mutable! And someone could come along and bash your computer with a hammer -- it would feel awfully mutabl

And the RAM your computer is writing everything to is mutable! And someone could come along and bash your computer with a hammer -- it would feel awfully mutable then! Everything is mutable if you consider the upcoming heat death of the universe. The point is that within the abstraction you're working in, recursion is entirely immutable, and loops are not. Good programmers selectively forget about stack pointers and RAM and the heat death of the universe when they're writing code -- they put on the correct "costume" for the part of code they're in and they never go "out of character". Worrying about the stack pointer is like having your Starbucks cup in the shot of Game of Thrones. Danaerys Targaryen doesn't know WTF Starbucks is and your programming avatar should not know WTF a stack pointer is.