It depends on what you're doing. If parts of the giant function are only reading the buffer, than you can just pass it as a const T& to your smaller inner function. If the inner function is modifying it, then i'd still pass it in, just as a T&. Or maybe I'd define an immediately invoked lambda that captures the buffer by ref. Functions are a tool for defining interfaces to pieces of logic - maybe I'm not as smart as Carmack and I don't have such a huge working memory, but I just can't keep more than 3-4 concepts in my head at the same time. Functions let you isolate those concepts and only think about their interface, rather than their internals.
I think the principle behind Carmack's letter is that factoring into multiple functions that all touch the same state is an illusion of reducing the burden on your memory. They still interact with each other via that state.
Pure functions, or your const T& situation, actually create smaller arenas of state. Splitting out multiple functions operating on the same object does not.
